Fdtxjr

Built-In Shelves/Bookcases - IKEA vs Built

Good allowance savings plan?

What is the chance of making a successful appeal to dismissal decision from a PhD program after failing the qualifying exam in the 2nd attempt?

What is the likely impact of grounding an entire aircraft series?

Do items de-spawn in Diablo?

Unreachable code, but reachable with exception

Space in array system equations

A three room house but a three headED dog

BitNot does not flip bits in the way I expected

2×2×2 rubik's cube corner is twisted!

Fourth person (in Slavey language)

How do anti-virus programs start at Windows boot?

Accountant/ lawyer will not return my call

How strictly should I take "Candidates must be local"?

Is it true that real estate prices mainly go up?

infinitive telling the purpose

My story is written in English, but is set in my home country. What language should I use for the dialogue?

Peter's Strange Word

They call me Inspector Morse

Subset counting for even numbers

What is the meaning of triple curly braces in phtml template files? When and how do we use them?

Force user to remove USB token

Solving "Resistance between two nodes on a grid" problem in Mathematica

How to pass a string to a command that expects a file?

Is $f(t) = e^X(t)$ continuous when matrix $X(t)$ is continuous?

show $int_0^1 f(t)g(t) dt$ is a non-degenerate scalar productClassification theorem for vector spacesThe vector-valued distribution of compact supportDerivations on the spaces of continuous functions form an infinite dimensional vector space(generalized tangent space)Example of element of double dual that is not an evaluation mapClarification Question on meaning of 2-dimensional Rotation MatrixContinuous analogy of the matrix inversionDoes value of differentiation as infinity implies continuity?Prove that the spectral radius $rho(A)$ is a continuous function, where $A$ is a square matrix.Continuity of $textrmargmin$ set-valued mapping

0

$begingroup$

I think $f(t) = e^X(t)$ is continuous over $t in mathbbR$ when the complex matrix valued mapping $tmapsto X(t)$ is continuous - regardless of whether $X$ is infinite or finite dimension. I tried to think of a proof, but without much success.

The hard part is the infinite-dimensional case, and I do not know what a proof could look like.

real-analysis linear-algebra functional-analysis continuity matrix-exponential

share|cite|improve this question

edited 2 days ago

Rodrigo de Azevedo

13k41960

asked 2 days ago

Lucia GuzheimLucia Guzheim

134

New contributor

Lucia Guzheim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  The composed of two continuous maps is continuous.
  $endgroup$
  – Gustave
  2 days ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Gustave: So you need to show $A mapsto e^A$ is continuous. For marix $A$ or bounded operator $A$ it is clear. But the OP does not spell out his/her assumptions. Physicists talk about semigroups of unbounded operators, for example.
  $endgroup$
  – GEdgar
  2 days ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @GEdgar A semigroup by definition is continuous, we don't talk here about the $X(t)$ as operator but as one variable function. Cordially.
  $endgroup$
  – Gustave
  2 days ago
  

  
  
  
  

add a comment | 

0

$begingroup$

I think $f(t) = e^X(t)$ is continuous over $t in mathbbR$ when the complex matrix valued mapping $tmapsto X(t)$ is continuous - regardless of whether $X$ is infinite or finite dimension. I tried to think of a proof, but without much success.

The hard part is the infinite-dimensional case, and I do not know what a proof could look like.

real-analysis linear-algebra functional-analysis continuity matrix-exponential

share|cite|improve this question

edited 2 days ago

Rodrigo de Azevedo

13k41960

asked 2 days ago

Lucia GuzheimLucia Guzheim

134

New contributor

Lucia Guzheim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  The composed of two continuous maps is continuous.
  $endgroup$
  – Gustave
  2 days ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Gustave: So you need to show $A mapsto e^A$ is continuous. For marix $A$ or bounded operator $A$ it is clear. But the OP does not spell out his/her assumptions. Physicists talk about semigroups of unbounded operators, for example.
  $endgroup$
  – GEdgar
  2 days ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @GEdgar A semigroup by definition is continuous, we don't talk here about the $X(t)$ as operator but as one variable function. Cordially.
  $endgroup$
  – Gustave
  2 days ago
  

  
  
  
  

add a comment | 

$begingroup$

I think $f(t) = e^X(t)$ is continuous over $t in mathbbR$ when the complex matrix valued mapping $tmapsto X(t)$ is continuous - regardless of whether $X$ is infinite or finite dimension. I tried to think of a proof, but without much success.

The hard part is the infinite-dimensional case, and I do not know what a proof could look like.

real-analysis linear-algebra functional-analysis continuity matrix-exponential

share|cite|improve this question

edited 2 days ago

Rodrigo de Azevedo

13k41960

asked 2 days ago

Lucia GuzheimLucia Guzheim

134

New contributor

Lucia Guzheim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

edited 2 days ago

Rodrigo de Azevedo

13k41960

asked 2 days ago

Lucia GuzheimLucia Guzheim

134

New contributor

Lucia Guzheim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

edited 2 days ago

Rodrigo de Azevedo

13k41960

asked 2 days ago

Lucia GuzheimLucia Guzheim

134

New contributor

Lucia Guzheim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

edited 2 days ago

Rodrigo de Azevedo

13k41960

edited 2 days ago

Rodrigo de Azevedo

13k41960

asked 2 days ago

Lucia GuzheimLucia Guzheim

134

New contributor

Lucia Guzheim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 2 days ago

Lucia GuzheimLucia Guzheim

134