What problems can we solve using linear algebra? [closed]

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I thought that linear algebra is a tool for solving systems of linear equations, but this can be done without most of linear algebra. That is, we just have to know matrix and the gaussian elimination and we don't have to know vector space, linear map, determinant, dimension, etc...

If we learn linear algebra, what problems can we solve other than systems of linear equations?

linear-algebra soft-question motivation

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asked Jul 21 at 2:47

satoukibi

16016

closed as too broad by Lord Shark the Unknown, zipirovich, John Ma, Taroccoesbrocco, Mostafa Ayaz Jul 21 at 18:43

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  bookstore.ams.org/stml-53
  – Lord Shark the Unknown
  Jul 21 at 2:51
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  to solve systems of differential equations, or polynomial, or algebraic etc
  – janmarqz
  Jul 21 at 3:06
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Founding what was going to become a multi-billion corporation is a pretty cool application of linear algebra.
  – zipirovich
  Jul 21 at 3:15
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

I thought that linear algebra is a tool for solving systems of linear equations, but this can be done without most of linear algebra. That is, we just have to know matrix and the gaussian elimination and we don't have to know vector space, linear map, determinant, dimension, etc...

If we learn linear algebra, what problems can we solve other than systems of linear equations?

linear-algebra soft-question motivation

share|cite|improve this question

asked Jul 21 at 2:47

satoukibi

16016

closed as too broad by Lord Shark the Unknown, zipirovich, John Ma, Taroccoesbrocco, Mostafa Ayaz Jul 21 at 18:43

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  bookstore.ams.org/stml-53
  – Lord Shark the Unknown
  Jul 21 at 2:51
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  to solve systems of differential equations, or polynomial, or algebraic etc
  – janmarqz
  Jul 21 at 3:06
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Founding what was going to become a multi-billion corporation is a pretty cool application of linear algebra.
  – zipirovich
  Jul 21 at 3:15
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

up vote
0
down vote

favorite

I thought that linear algebra is a tool for solving systems of linear equations, but this can be done without most of linear algebra. That is, we just have to know matrix and the gaussian elimination and we don't have to know vector space, linear map, determinant, dimension, etc...

If we learn linear algebra, what problems can we solve other than systems of linear equations?

linear-algebra soft-question motivation

share|cite|improve this question

asked Jul 21 at 2:47

satoukibi

16016

I thought that linear algebra is a tool for solving systems of linear equations, but this can be done without most of linear algebra. That is, we just have to know matrix and the gaussian elimination and we don't have to know vector space, linear map, determinant, dimension, etc...

If we learn linear algebra, what problems can we solve other than systems of linear equations?

linear-algebra soft-question motivation

share|cite|improve this question

asked Jul 21 at 2:47

satoukibi

16016

share|cite|improve this question

share|cite|improve this question

asked Jul 21 at 2:47

satoukibi

16016

asked Jul 21 at 2:47

satoukibi

16016

asked Jul 21 at 2:47

satoukibi

16016

16016

closed as too broad by Lord Shark the Unknown, zipirovich, John Ma, Taroccoesbrocco, Mostafa Ayaz Jul 21 at 18:43

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

closed as too broad by Lord Shark the Unknown, zipirovich, John Ma, Taroccoesbrocco, Mostafa Ayaz Jul 21 at 18:43

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  bookstore.ams.org/stml-53
  – Lord Shark the Unknown
  Jul 21 at 2:51
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  to solve systems of differential equations, or polynomial, or algebraic etc
  – janmarqz
  Jul 21 at 3:06
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Founding what was going to become a multi-billion corporation is a pretty cool application of linear algebra.
  – zipirovich
  Jul 21 at 3:15
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  bookstore.ams.org/stml-53
  – Lord Shark the Unknown
  Jul 21 at 2:51
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  to solve systems of differential equations, or polynomial, or algebraic etc
  – janmarqz
  Jul 21 at 3:06
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Founding what was going to become a multi-billion corporation is a pretty cool application of linear algebra.
  – zipirovich
  Jul 21 at 3:15
  

  
  
  
  

2

2

bookstore.ams.org/stml-53
– Lord Shark the Unknown
Jul 21 at 2:51

bookstore.ams.org/stml-53
– Lord Shark the Unknown
Jul 21 at 2:51

1

1

to solve systems of differential equations, or polynomial, or algebraic etc
– janmarqz
Jul 21 at 3:06

to solve systems of differential equations, or polynomial, or algebraic etc
– janmarqz
Jul 21 at 3:06

Founding what was going to become a multi-billion corporation is a pretty cool application of linear algebra.
– zipirovich
Jul 21 at 3:15

Founding what was going to become a multi-billion corporation is a pretty cool application of linear algebra.
– zipirovich
Jul 21 at 3:15

add a comment | 

4 Answers
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1
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accepted

In my numerical linear algebra class my professor stated that 70% of problems can be summarized as the $Ax=b$ problem and the eigenvalue problem. The rest of the problems are slight variations of these problems.

There are a lot of applications. My advisor worked on stabilizing a method for solving hyperbolic PDEs and later he made them faster using FFTs and the SVD.

If you look at most websites like for instance Facebook, Amazon, Netflix or other places they use recommender systems based on linear algebra. These use the SVD algorithm to find users and items that are near other users or items and recommend them to other people.

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answered Jul 21 at 3:54

RHowe

1,000815

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Linear Systems, Manifold Systems or systems that are almost linear. Hence, you are speaking about systems in which the configuration space is either a hypersurface i.e $mathbbR^N$ for some $N$ or a manifold $M^N$ where $N$ denotes the dimension. Lastly, by almost linear this means you don't have to be a manifold but the underlying data set relates strongly enough to define tangent planes i.e linear maps.

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answered Jul 21 at 2:54

Faraad Armwood

7,4292619

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My favorite application of linear algebra is in computer graphics. Using eigenvalue decomposition allows for quick computation of large powers of matrices.

In computer graphics, things like 3D models and plants are modeled using triangles all stuck together, and then they're smoothed out using a process involving taking large powers of matrices. Linear algebra makes this very quick, which allows us to play 3D games at a reasonable rate!!

For more description, see this video :)

share|cite|improve this answer

edited Jul 21 at 3:57

answered Jul 21 at 3:51

Sambo

1,2561427

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There was a comment years ago to the effect of "Why do we study linear algebra? Because linear algebra is easy and many problems can be reduced to it." Solutions to homogeneous differential equations form a vector space as do solutions to homogeneous recurrence relations. Coupled differential equations become much simpler if you change the basis to decouple them. All of Fourier analysis is essentially a change of basis in the vector space of functions. The fact that $int (af(x)+bg(x))dx=aint f(x)dx+bint g(x)dx$ reflects that the integrable functions form a vector space.

share|cite|improve this answer

answered Jul 21 at 4:01

Ross Millikan

276k21186352

add a comment | 

4 Answers
4

active

oldest

votes

4 Answers
4

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
1
down vote



accepted

In my numerical linear algebra class my professor stated that 70% of problems can be summarized as the $Ax=b$ problem and the eigenvalue problem. The rest of the problems are slight variations of these problems.

There are a lot of applications. My advisor worked on stabilizing a method for solving hyperbolic PDEs and later he made them faster using FFTs and the SVD.

If you look at most websites like for instance Facebook, Amazon, Netflix or other places they use recommender systems based on linear algebra. These use the SVD algorithm to find users and items that are near other users or items and recommend them to other people.

share|cite|improve this answer

answered Jul 21 at 3:54

RHowe

1,000815

add a comment | 

up vote
1
down vote



accepted

In my numerical linear algebra class my professor stated that 70% of problems can be summarized as the $Ax=b$ problem and the eigenvalue problem. The rest of the problems are slight variations of these problems.

There are a lot of applications. My advisor worked on stabilizing a method for solving hyperbolic PDEs and later he made them faster using FFTs and the SVD.

If you look at most websites like for instance Facebook, Amazon, Netflix or other places they use recommender systems based on linear algebra. These use the SVD algorithm to find users and items that are near other users or items and recommend them to other people.

share|cite|improve this answer

answered Jul 21 at 3:54

RHowe

1,000815

add a comment | 

up vote
1
down vote



accepted

up vote
1
down vote



accepted

In my numerical linear algebra class my professor stated that 70% of problems can be summarized as the $Ax=b$ problem and the eigenvalue problem. The rest of the problems are slight variations of these problems.

There are a lot of applications. My advisor worked on stabilizing a method for solving hyperbolic PDEs and later he made them faster using FFTs and the SVD.

If you look at most websites like for instance Facebook, Amazon, Netflix or other places they use recommender systems based on linear algebra. These use the SVD algorithm to find users and items that are near other users or items and recommend them to other people.

share|cite|improve this answer

answered Jul 21 at 3:54

RHowe

1,000815

In my numerical linear algebra class my professor stated that 70% of problems can be summarized as the $Ax=b$ problem and the eigenvalue problem. The rest of the problems are slight variations of these problems.

There are a lot of applications. My advisor worked on stabilizing a method for solving hyperbolic PDEs and later he made them faster using FFTs and the SVD.

If you look at most websites like for instance Facebook, Amazon, Netflix or other places they use recommender systems based on linear algebra. These use the SVD algorithm to find users and items that are near other users or items and recommend them to other people.

share|cite|improve this answer

answered Jul 21 at 3:54

RHowe

1,000815

share|cite|improve this answer

share|cite|improve this answer

answered Jul 21 at 3:54

RHowe

1,000815

answered Jul 21 at 3:54

RHowe

1,000815

answered Jul 21 at 3:54

RHowe

1,000815

1,000815

add a comment | 

add a comment | 

up vote
0
down vote

Linear Systems, Manifold Systems or systems that are almost linear. Hence, you are speaking about systems in which the configuration space is either a hypersurface i.e $mathbbR^N$ for some $N$ or a manifold $M^N$ where $N$ denotes the dimension. Lastly, by almost linear this means you don't have to be a manifold but the underlying data set relates strongly enough to define tangent planes i.e linear maps.

share|cite|improve this answer

answered Jul 21 at 2:54

Faraad Armwood

7,4292619

add a comment | 

up vote
0
down vote

Linear Systems, Manifold Systems or systems that are almost linear. Hence, you are speaking about systems in which the configuration space is either a hypersurface i.e $mathbbR^N$ for some $N$ or a manifold $M^N$ where $N$ denotes the dimension. Lastly, by almost linear this means you don't have to be a manifold but the underlying data set relates strongly enough to define tangent planes i.e linear maps.

share|cite|improve this answer

answered Jul 21 at 2:54

Faraad Armwood

7,4292619

add a comment | 

up vote
0
down vote

up vote
0
down vote

Linear Systems, Manifold Systems or systems that are almost linear. Hence, you are speaking about systems in which the configuration space is either a hypersurface i.e $mathbbR^N$ for some $N$ or a manifold $M^N$ where $N$ denotes the dimension. Lastly, by almost linear this means you don't have to be a manifold but the underlying data set relates strongly enough to define tangent planes i.e linear maps.

share|cite|improve this answer

answered Jul 21 at 2:54

Faraad Armwood

7,4292619

Linear Systems, Manifold Systems or systems that are almost linear. Hence, you are speaking about systems in which the configuration space is either a hypersurface i.e $mathbbR^N$ for some $N$ or a manifold $M^N$ where $N$ denotes the dimension. Lastly, by almost linear this means you don't have to be a manifold but the underlying data set relates strongly enough to define tangent planes i.e linear maps.

share|cite|improve this answer

answered Jul 21 at 2:54

Faraad Armwood

7,4292619

share|cite|improve this answer

share|cite|improve this answer

answered Jul 21 at 2:54

Faraad Armwood

7,4292619

answered Jul 21 at 2:54

Faraad Armwood

7,4292619

answered Jul 21 at 2:54

Faraad Armwood

7,4292619

7,4292619

add a comment | 

add a comment | 

up vote
0
down vote

My favorite application of linear algebra is in computer graphics. Using eigenvalue decomposition allows for quick computation of large powers of matrices.

In computer graphics, things like 3D models and plants are modeled using triangles all stuck together, and then they're smoothed out using a process involving taking large powers of matrices. Linear algebra makes this very quick, which allows us to play 3D games at a reasonable rate!!

For more description, see this video :)

share|cite|improve this answer

edited Jul 21 at 3:57

answered Jul 21 at 3:51

Sambo

1,2561427

add a comment | 

up vote
0
down vote

My favorite application of linear algebra is in computer graphics. Using eigenvalue decomposition allows for quick computation of large powers of matrices.

In computer graphics, things like 3D models and plants are modeled using triangles all stuck together, and then they're smoothed out using a process involving taking large powers of matrices. Linear algebra makes this very quick, which allows us to play 3D games at a reasonable rate!!

For more description, see this video :)

share|cite|improve this answer

edited Jul 21 at 3:57

answered Jul 21 at 3:51

Sambo

1,2561427

add a comment | 

up vote
0
down vote

up vote
0
down vote

My favorite application of linear algebra is in computer graphics. Using eigenvalue decomposition allows for quick computation of large powers of matrices.

In computer graphics, things like 3D models and plants are modeled using triangles all stuck together, and then they're smoothed out using a process involving taking large powers of matrices. Linear algebra makes this very quick, which allows us to play 3D games at a reasonable rate!!

For more description, see this video :)

share|cite|improve this answer

edited Jul 21 at 3:57

answered Jul 21 at 3:51

Sambo

1,2561427

My favorite application of linear algebra is in computer graphics. Using eigenvalue decomposition allows for quick computation of large powers of matrices.

In computer graphics, things like 3D models and plants are modeled using triangles all stuck together, and then they're smoothed out using a process involving taking large powers of matrices. Linear algebra makes this very quick, which allows us to play 3D games at a reasonable rate!!

For more description, see this video :)

share|cite|improve this answer

edited Jul 21 at 3:57

answered Jul 21 at 3:51

Sambo

1,2561427

share|cite|improve this answer

share|cite|improve this answer

edited Jul 21 at 3:57

edited Jul 21 at 3:57

edited Jul 21 at 3:57

answered Jul 21 at 3:51

Sambo

1,2561427

answered Jul 21 at 3:51

Sambo

1,2561427

answered Jul 21 at 3:51

Sambo

1,2561427

1,2561427

add a comment | 

add a comment | 

up vote
0
down vote

There was a comment years ago to the effect of "Why do we study linear algebra? Because linear algebra is easy and many problems can be reduced to it." Solutions to homogeneous differential equations form a vector space as do solutions to homogeneous recurrence relations. Coupled differential equations become much simpler if you change the basis to decouple them. All of Fourier analysis is essentially a change of basis in the vector space of functions. The fact that $int (af(x)+bg(x))dx=aint f(x)dx+bint g(x)dx$ reflects that the integrable functions form a vector space.

share|cite|improve this answer

answered Jul 21 at 4:01

Ross Millikan

276k21186352

add a comment | 

up vote
0
down vote

There was a comment years ago to the effect of "Why do we study linear algebra? Because linear algebra is easy and many problems can be reduced to it." Solutions to homogeneous differential equations form a vector space as do solutions to homogeneous recurrence relations. Coupled differential equations become much simpler if you change the basis to decouple them. All of Fourier analysis is essentially a change of basis in the vector space of functions. The fact that $int (af(x)+bg(x))dx=aint f(x)dx+bint g(x)dx$ reflects that the integrable functions form a vector space.

share|cite|improve this answer

answered Jul 21 at 4:01

Ross Millikan

276k21186352

add a comment | 

up vote
0
down vote

up vote
0
down vote

There was a comment years ago to the effect of "Why do we study linear algebra? Because linear algebra is easy and many problems can be reduced to it." Solutions to homogeneous differential equations form a vector space as do solutions to homogeneous recurrence relations. Coupled differential equations become much simpler if you change the basis to decouple them. All of Fourier analysis is essentially a change of basis in the vector space of functions. The fact that $int (af(x)+bg(x))dx=aint f(x)dx+bint g(x)dx$ reflects that the integrable functions form a vector space.

share|cite|improve this answer

answered Jul 21 at 4:01

Ross Millikan

276k21186352

There was a comment years ago to the effect of "Why do we study linear algebra? Because linear algebra is easy and many problems can be reduced to it." Solutions to homogeneous differential equations form a vector space as do solutions to homogeneous recurrence relations. Coupled differential equations become much simpler if you change the basis to decouple them. All of Fourier analysis is essentially a change of basis in the vector space of functions. The fact that $int (af(x)+bg(x))dx=aint f(x)dx+bint g(x)dx$ reflects that the integrable functions form a vector space.

share|cite|improve this answer

answered Jul 21 at 4:01

Ross Millikan

276k21186352

share|cite|improve this answer

share|cite|improve this answer

answered Jul 21 at 4:01

Ross Millikan

276k21186352

answered Jul 21 at 4:01

Ross Millikan

276k21186352

answered Jul 21 at 4:01

Ross Millikan

276k21186352

276k21186352

add a comment | 

add a comment |