Show that $Vert xVert_* := Vert UxVert $ is a vector norm [closed]
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Let $Vert * Vert$ be a Vectornorm in $mathbb{R}^n$ or $mathbb{C}^n$ and $U in mathbb{R}^{ntimes n}$ a regular matrix.
How can I show that $Vert xVert_* := Vert UxVert $ is also a Vectornorm? For example if $Vert * Vert$ is the Euclidean norm what would the explicit formula for the induced matrix norm look like and in what relation would that be to the spectral norm?
linear-algebra norm
asked Dec 2 at 14:28
rsgasae
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closed as off-topic by user302797, GNUSupporter 8964民主女神 地下教會, Brahadeesh, Yanko, José Carlos Santos Dec 2 at 14:56
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user302797, GNUSupporter 8964民主女神 地下教會, Brahadeesh, Yanko, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
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Let $Vert * Vert$ be a Vectornorm in $mathbb{R}^n$ or $mathbb{C}^n$ and $U in mathbb{R}^{ntimes n}$ a regular matrix.
How can I show that $Vert xVert_* := Vert UxVert $ is also a Vectornorm? For example if $Vert * Vert$ is the Euclidean norm what would the explicit formula for the induced matrix norm look like and in what relation would that be to the spectral norm?
linear-algebra norm
asked Dec 2 at 14:28
rsgasae
22
New contributor
rsgasae is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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closed as off-topic by user302797, GNUSupporter 8964民主女神 地下教會, Brahadeesh, Yanko, José Carlos Santos Dec 2 at 14:56
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user302797, GNUSupporter 8964民主女神 地下教會, Brahadeesh, Yanko, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
Define "regular matrix"?
– Henno Brandsma
Dec 2 at 14:34
@HennoBrandsma It's an alternative name for “invertible matrix”.
– egreg
Dec 2 at 14:36
2
Showing it is a norm is just applying the definitions.
– egreg
Dec 2 at 14:37
add a comment |
up vote
-1
down vote
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up vote
-1
down vote
favorite
Let $Vert * Vert$ be a Vectornorm in $mathbb{R}^n$ or $mathbb{C}^n$ and $U in mathbb{R}^{ntimes n}$ a regular matrix.
How can I show that $Vert xVert_* := Vert UxVert $ is also a Vectornorm? For example if $Vert * Vert$ is the Euclidean norm what would the explicit formula for the induced matrix norm look like and in what relation would that be to the spectral norm?
linear-algebra norm
asked Dec 2 at 14:28
rsgasae
22
New contributor
rsgasae is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Let $Vert * Vert$ be a Vectornorm in $mathbb{R}^n$ or $mathbb{C}^n$ and $U in mathbb{R}^{ntimes n}$ a regular matrix.
How can I show that $Vert xVert_* := Vert UxVert $ is also a Vectornorm? For example if $Vert * Vert$ is the Euclidean norm what would the explicit formula for the induced matrix norm look like and in what relation would that be to the spectral norm?
linear-algebra norm
linear-algebra norm
asked Dec 2 at 14:28
rsgasae
22
New contributor
rsgasae is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Dec 2 at 14:28
rsgasae
22
New contributor
rsgasae is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Dec 2 at 14:28
rsgasae
22
New contributor
rsgasae is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Dec 2 at 14:28
rsgasae
22
asked Dec 2 at 14:28
rsgasae
22
22
New contributor
rsgasae is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
rsgasae is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
rsgasae is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
closed as off-topic by user302797, GNUSupporter 8964民主女神 地下教會, Brahadeesh, Yanko, José Carlos Santos Dec 2 at 14:56
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user302797, GNUSupporter 8964民主女神 地下教會, Brahadeesh, Yanko, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by user302797, GNUSupporter 8964民主女神 地下教會, Brahadeesh, Yanko, José Carlos Santos Dec 2 at 14:56
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user302797, GNUSupporter 8964民主女神 地下教會, Brahadeesh, Yanko, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
Define "regular matrix"?
– Henno Brandsma
Dec 2 at 14:34
@HennoBrandsma It's an alternative name for “invertible matrix”.
– egreg
Dec 2 at 14:36
2
Showing it is a norm is just applying the definitions.
– egreg
Dec 2 at 14:37
add a comment |
Define "regular matrix"?
– Henno Brandsma
Dec 2 at 14:34
@HennoBrandsma It's an alternative name for “invertible matrix”.
– egreg
Dec 2 at 14:36
2
Showing it is a norm is just applying the definitions.
– egreg
Dec 2 at 14:37
Define "regular matrix"?
– Henno Brandsma
Dec 2 at 14:34
Define "regular matrix"?
– Henno Brandsma
Dec 2 at 14:34
@HennoBrandsma It's an alternative name for “invertible matrix”.
– egreg
Dec 2 at 14:36
@HennoBrandsma It's an alternative name for “invertible matrix”.
– egreg
Dec 2 at 14:36
2
2
Showing it is a norm is just applying the definitions.
– egreg
Dec 2 at 14:37
Showing it is a norm is just applying the definitions.
– egreg
Dec 2 at 14:37
add a comment |
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Define "regular matrix"?
– Henno Brandsma
Dec 2 at 14:34
@HennoBrandsma It's an alternative name for “invertible matrix”.
– egreg
Dec 2 at 14:36
2
Showing it is a norm is just applying the definitions.
– egreg
Dec 2 at 14:37