Extract a vector that is in the middle of a matrix equation

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So I have the following problem that is giving me a hard time for some reason:

I have a matrix equation of the form $RA(I-alpha e')$ where

• $R$ is an $n times n$ matrix


• $A$ is a triangular $n times n$ matrix


• $I$ is the $n times n$ identity matrix


• $alpha$ is a $n times 1$ vector and


• $e'$ is a $1 times n$ vector of ones.

Clearly this equation is some linear mapping $f(alpha)$. I am now wondering if (and if yes how) it is possible to rewrite this equation into the form.

$f(alpha) = Xalpha$?

I have been thinking and trying and researching but I wasn't able to come up with a good answer.

Thank you!
Rob

linear-transformations matrix-equations

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asked Jul 20 at 17:09

korpuskel91

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So I have the following problem that is giving me a hard time for some reason:

I have a matrix equation of the form $RA(I-alpha e')$ where

• $R$ is an $n times n$ matrix


• $A$ is a triangular $n times n$ matrix


• $I$ is the $n times n$ identity matrix


• $alpha$ is a $n times 1$ vector and


• $e'$ is a $1 times n$ vector of ones.

Clearly this equation is some linear mapping $f(alpha)$. I am now wondering if (and if yes how) it is possible to rewrite this equation into the form.

$f(alpha) = Xalpha$?

I have been thinking and trying and researching but I wasn't able to come up with a good answer.

Thank you!
Rob

linear-transformations matrix-equations

share|cite|improve this question

asked Jul 20 at 17:09

korpuskel91

83

add a comment | 

up vote
1
down vote

favorite

up vote
1
down vote

favorite

So I have the following problem that is giving me a hard time for some reason:

I have a matrix equation of the form $RA(I-alpha e')$ where

• $R$ is an $n times n$ matrix


• $A$ is a triangular $n times n$ matrix


• $I$ is the $n times n$ identity matrix


• $alpha$ is a $n times 1$ vector and


• $e'$ is a $1 times n$ vector of ones.

Clearly this equation is some linear mapping $f(alpha)$. I am now wondering if (and if yes how) it is possible to rewrite this equation into the form.

$f(alpha) = Xalpha$?

I have been thinking and trying and researching but I wasn't able to come up with a good answer.

Thank you!
Rob

linear-transformations matrix-equations

share|cite|improve this question

asked Jul 20 at 17:09

korpuskel91

83

So I have the following problem that is giving me a hard time for some reason:

I have a matrix equation of the form $RA(I-alpha e')$ where

• $R$ is an $n times n$ matrix


• $A$ is a triangular $n times n$ matrix


• $I$ is the $n times n$ identity matrix


• $alpha$ is a $n times 1$ vector and


• $e'$ is a $1 times n$ vector of ones.

Clearly this equation is some linear mapping $f(alpha)$. I am now wondering if (and if yes how) it is possible to rewrite this equation into the form.

$f(alpha) = Xalpha$?

I have been thinking and trying and researching but I wasn't able to come up with a good answer.

Thank you!
Rob

linear-transformations matrix-equations

share|cite|improve this question

asked Jul 20 at 17:09

korpuskel91

83

share|cite|improve this question

share|cite|improve this question

asked Jul 20 at 17:09

korpuskel91

83

asked Jul 20 at 17:09

korpuskel91

83

asked Jul 20 at 17:09

korpuskel91

83

83

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add a comment | 

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I don't think so, the second equation you're writing should output a vector (if $X$ is a matrix), while the first equation you're writing should output a matrix. Also the first equation is not linear but affine ($f(v+w)neq f(v)+f(w)$ for $v,winmathbbR^ntimes1$).

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answered Jul 20 at 17:34

Stef

61

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1 Answer
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active

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1 Answer
1

active

oldest

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oldest

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up vote
0
down vote

I don't think so, the second equation you're writing should output a vector (if $X$ is a matrix), while the first equation you're writing should output a matrix. Also the first equation is not linear but affine ($f(v+w)neq f(v)+f(w)$ for $v,winmathbbR^ntimes1$).

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answered Jul 20 at 17:34

Stef

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up vote
0
down vote

I don't think so, the second equation you're writing should output a vector (if $X$ is a matrix), while the first equation you're writing should output a matrix. Also the first equation is not linear but affine ($f(v+w)neq f(v)+f(w)$ for $v,winmathbbR^ntimes1$).

share|cite|improve this answer

answered Jul 20 at 17:34

Stef

61

add a comment | 

up vote
0
down vote

up vote
0
down vote

I don't think so, the second equation you're writing should output a vector (if $X$ is a matrix), while the first equation you're writing should output a matrix. Also the first equation is not linear but affine ($f(v+w)neq f(v)+f(w)$ for $v,winmathbbR^ntimes1$).

share|cite|improve this answer

answered Jul 20 at 17:34

Stef

61

I don't think so, the second equation you're writing should output a vector (if $X$ is a matrix), while the first equation you're writing should output a matrix. Also the first equation is not linear but affine ($f(v+w)neq f(v)+f(w)$ for $v,winmathbbR^ntimes1$).

share|cite|improve this answer

answered Jul 20 at 17:34

Stef

61

share|cite|improve this answer

share|cite|improve this answer

answered Jul 20 at 17:34

Stef

61

answered Jul 20 at 17:34

Stef

61

answered Jul 20 at 17:34

Stef

61

61

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add a comment | 

 

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