# Tagged Questions

For any topic related to matrices. This includes: systems of linear equations, eigenvalues and eigenvectors (diagonalization, triangularization), determinant, trace, characteristic polynomial, adjugate, transpose, Jordan normal form, matrix algorithms (e.g. LU, Gauss elimination, SVD, QR), ...

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### Mean value for $\tiny\left( \begin{array}{cc} X & X \\ -X & 1-X \\ \end{array} \right)$

We have a matrix $$\left( \begin{array}{cc} X & X \\ -X & 1-X \\ \end{array} \right)$$ where $X$ is a random variable between $0$ and $1$. I heard about "random matrices". Is it an ...
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### Commutative Monoid - matrix set

Let $M$={$\begin{bmatrix} a & b & c \\ c & a & b \\ b & c & a \end{bmatrix}|a,b,c\in \mathbb{R}, a+b+c=0$}. The matrices in $M$ are a special kind of Toeplitz matrices (...
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### rotating a rectangle via a rotation matrix

I want to rotate a 2D rectangle using a rotation matrix. After the rotation, I want the points (x, y) of the rectangle to be: ...
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### Given $A^2-4A+I=0$, show that $A^3=15A-4I$

If have a question like this , can we using equation method or deduction method to answer the question?? Or we need to answer the question by substituting the matrix??
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### Proof for $\mathbf{M}$ unitary if $||\mathbf{M}\mathbf{v}|| = ||\mathbf{v}||$

Let $\mathbf{M} \in \mathbb{F}^{n, n}$. Then $||\mathbf{M}\mathbf{v}|| = ||\mathbf{v}||$($\mathbf{v} \in \mathbb{F}^n$) implies that $\mathbf{M}$ is unitary. My question is, how to prove this theorem?...
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### Analytical result for element-wise vector division?

I have two vectors $$a=[a_1,a_2,...,a_n], b=[b_1,b_2,...,b_n]$$ Is it possible to express the result $$c=[a_1/b_1,a_2/b_2,...,a_n/b_n]$$ by some standard matrix operations such as matrix ...
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### how to calculate the projection of a vector onto a closed convex set? [duplicate]

suppose we have a vector $x \in \mathbb{R}^{n}$, and a closed convex set $C \in \mathbb{R}^{n}$. $C =\{x|Ax=b\}$ how to calculate the vector $y \in \mathbb{R}^{n}$, which is the projection of $x$ ...
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### $A$ a $n\times n$ matrix with real entries such that $A^3 = I$ but $A \ne I$

Let $A$ a $n \times n$ matrix with real entries such that $A^3 = I$ but $A \ne I$. a) Give an example that satisfies this conditions. b) what are the eigenvalues ​​of $A$? Well for $a)$ i ...
### Is there a matrix with real entries such that $A \ne I_2$ but $A^3 = I_2$.
Is there a matrix with real entries such that $A \ne I_2$ but $A^3 = I_2$. I've actually encountered with this post: $A$ a $n\times n$ matrix with real entries such that $A^3 = I$ but $A \ne I$ ...