List questions from matrix-equations

Published on 25 Mar 2026 - 7:53

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Linear Algebra - Find Matrix X

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How do you find all solutions to the matrix equation $XAX=A^T$?

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Is $A^TBA$ positive definite if and only if $A$ is nonsingular and $B$ is positive definite

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How to show infinite solutions of linear equation system?

Published on 07 Jun 2018 - 23:57

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Are there scalars $a, b,$ and $c$ such that $A.X = B$ has infinite solutions? And such that the system does not have solutions?

Published on 25 Mar 2026 - 23:38

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What is the structure of a matrix when all the eigenvalues are complex?

Published on 10 Jun 2018 - 15:35

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How to determine value of a matrix

Published on 11 Jun 2018 - 12:30

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What can be said about $A+A^T$ when $A$ has all eigenvalues on imaginary axis and A is not normal?

Published on 25 Mar 2026 - 9:26

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Derivative of exponential function wrt a vector

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How to find a basis for a subspace?

Published on 25 Mar 2026 - 18:46

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How to find basis for a subspace?

Published on 12 Jun 2018 - 14:40

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Lecture to solve 2nd order differential equation in matrix form.

Published on 12 Jun 2018 - 15:54

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Given matrices $A$ and $B$, solve $XA = B$

Published on 13 Jun 2018 - 6:15

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Find a matrix such that $XX'= I$

Published on 13 Jun 2018 - 11:42

List Question

Show that $(A^TA)^{-1} A^T$ minimizes $\mbox{Tr}(X^T X)$ over all matrices $X$ such that $XA = I$

Linear Algebra - Find Matrix X

How do you find all solutions to the matrix equation $XAX=A^T$?

Is $A^TBA$ positive definite if and only if $A$ is nonsingular and $B$ is positive definite

How to show infinite solutions of linear equation system?

Are there scalars $a, b,$ and $c$ such that $A.X = B$ has infinite solutions? And such that the system does not have solutions?

What is the structure of a matrix when all the eigenvalues are complex?

How to determine value of a matrix

What can be said about $A+A^T$ when $A$ has all eigenvalues on imaginary axis and A is not normal?

Derivative of exponential function wrt a vector

How to find a basis for a subspace?

How to find basis for a subspace?

Lecture to solve 2nd order differential equation in matrix form.

Given matrices $A$ and $B$, solve $XA = B$

Find a matrix such that $XX'= I$

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