Terminology in higher dimensional linear equations

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Given that $y=kx+d$ is called a linear relationship, are there established naming conventions when more variables are concerned?

The linear equation can be generalized by $b + sum a_ix_i = 0$ and the result should be a hyperplane. In the 2D case mentioned at the beginning, such a hyperplane is a line and I assume that linear relationship is derived from that. In the 3D case $z = ax + by +c$, the hyperplane results in a simple plane (example drawing), is that relationship called planar, analogous to the linear example?

linear-algebra geometry terminology

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asked Jul 27 at 12:44

Kreks

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Given that $y=kx+d$ is called a linear relationship, are there established naming conventions when more variables are concerned?

The linear equation can be generalized by $b + sum a_ix_i = 0$ and the result should be a hyperplane. In the 2D case mentioned at the beginning, such a hyperplane is a line and I assume that linear relationship is derived from that. In the 3D case $z = ax + by +c$, the hyperplane results in a simple plane (example drawing), is that relationship called planar, analogous to the linear example?

linear-algebra geometry terminology

share|cite|improve this question

asked Jul 27 at 12:44

Kreks

225

add a comment | 

up vote
1
down vote

favorite

up vote
1
down vote

favorite

Given that $y=kx+d$ is called a linear relationship, are there established naming conventions when more variables are concerned?

The linear equation can be generalized by $b + sum a_ix_i = 0$ and the result should be a hyperplane. In the 2D case mentioned at the beginning, such a hyperplane is a line and I assume that linear relationship is derived from that. In the 3D case $z = ax + by +c$, the hyperplane results in a simple plane (example drawing), is that relationship called planar, analogous to the linear example?

linear-algebra geometry terminology

share|cite|improve this question

asked Jul 27 at 12:44

Kreks

225

Given that $y=kx+d$ is called a linear relationship, are there established naming conventions when more variables are concerned?

The linear equation can be generalized by $b + sum a_ix_i = 0$ and the result should be a hyperplane. In the 2D case mentioned at the beginning, such a hyperplane is a line and I assume that linear relationship is derived from that. In the 3D case $z = ax + by +c$, the hyperplane results in a simple plane (example drawing), is that relationship called planar, analogous to the linear example?

linear-algebra geometry terminology

share|cite|improve this question

asked Jul 27 at 12:44

Kreks

225

share|cite|improve this question

share|cite|improve this question

asked Jul 27 at 12:44

Kreks

225

asked Jul 27 at 12:44

Kreks

225

asked Jul 27 at 12:44

Kreks

225

225

add a comment | 

add a comment | 

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In general, in $mathbbR^3$ for $cne 0$ the relation $z = ax + by +c$ represents an affine plane or simply a plane.

For $c=0$ we define $z = ax + by$ as a linear subspace of dimension $2$, that is a plane through the origin.

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edited Jul 27 at 13:27

answered Jul 27 at 13:22

gimusi

64.9k73583

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for pointing me towards affine planes, that will come in handy, but I still don't know if the relation between x, y and z is called a planar relation or not.
  – Kreks
  Jul 30 at 7:18
  

  
  
  
  

add a comment | 

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1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
-1
down vote

In general, in $mathbbR^3$ for $cne 0$ the relation $z = ax + by +c$ represents an affine plane or simply a plane.

For $c=0$ we define $z = ax + by$ as a linear subspace of dimension $2$, that is a plane through the origin.

share|cite|improve this answer

edited Jul 27 at 13:27

answered Jul 27 at 13:22

gimusi

64.9k73583

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for pointing me towards affine planes, that will come in handy, but I still don't know if the relation between x, y and z is called a planar relation or not.
  – Kreks
  Jul 30 at 7:18
  

  
  
  
  

add a comment | 

up vote
-1
down vote

In general, in $mathbbR^3$ for $cne 0$ the relation $z = ax + by +c$ represents an affine plane or simply a plane.

For $c=0$ we define $z = ax + by$ as a linear subspace of dimension $2$, that is a plane through the origin.

share|cite|improve this answer

edited Jul 27 at 13:27

answered Jul 27 at 13:22

gimusi

64.9k73583

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for pointing me towards affine planes, that will come in handy, but I still don't know if the relation between x, y and z is called a planar relation or not.
  – Kreks
  Jul 30 at 7:18
  

  
  
  
  

add a comment | 

up vote
-1
down vote

up vote
-1
down vote

In general, in $mathbbR^3$ for $cne 0$ the relation $z = ax + by +c$ represents an affine plane or simply a plane.

For $c=0$ we define $z = ax + by$ as a linear subspace of dimension $2$, that is a plane through the origin.

share|cite|improve this answer

edited Jul 27 at 13:27

answered Jul 27 at 13:22

gimusi

64.9k73583

In general, in $mathbbR^3$ for $cne 0$ the relation $z = ax + by +c$ represents an affine plane or simply a plane.

For $c=0$ we define $z = ax + by$ as a linear subspace of dimension $2$, that is a plane through the origin.

share|cite|improve this answer

edited Jul 27 at 13:27

answered Jul 27 at 13:22

gimusi

64.9k73583

share|cite|improve this answer

share|cite|improve this answer

edited Jul 27 at 13:27

edited Jul 27 at 13:27

edited Jul 27 at 13:27

answered Jul 27 at 13:22

gimusi

64.9k73583

answered Jul 27 at 13:22

gimusi

64.9k73583

answered Jul 27 at 13:22

gimusi

64.9k73583

64.9k73583

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for pointing me towards affine planes, that will come in handy, but I still don't know if the relation between x, y and z is called a planar relation or not.
  – Kreks
  Jul 30 at 7:18
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for pointing me towards affine planes, that will come in handy, but I still don't know if the relation between x, y and z is called a planar relation or not.
  – Kreks
  Jul 30 at 7:18
  

  
  
  
  

Thanks for pointing me towards affine planes, that will come in handy, but I still don't know if the relation between x, y and z is called a planar relation or not.
– Kreks
Jul 30 at 7:18

Thanks for pointing me towards affine planes, that will come in handy, but I still don't know if the relation between x, y and z is called a planar relation or not.
– Kreks
Jul 30 at 7:18

add a comment | 

 

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