# Questions tagged [matrices]

For any topic related to matrices. This includes: systems of linear equations, eigenvalues and eigenvectors (diagonalization, triangularization), determinant, trace, characteristic polynomial, adjugate and adjoint, transpose, Jordan normal form, matrix algorithms (e.g. LU, Gauss elimination, SVD, QR), invariant factors, quadratic forms, etc. For questions specifically concerning matrix equations, use the (matrix-equations) tag.

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### Can someone help me, to compute by hand $Ax=b$ where $A$ is a $5\times5$ Matrix and $b=(1,1,1,1,1)$ transposed

Using Cholesky decomposition i have L and L transposed,how can i solve $Ax=b$ without using inverses? $A$ is a $5\times 5$ Matrix $b=(1,1,1,1,1)^t$ Another question, How would you easily compute the ...
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### What set of matrices $X,Y$ satisfy $X \circ Y = X P Y$ for at least one permutation matrix $P$?

Suppose we have three $n \times n$ matrices $X,Y,P$ where $X,Y \in \mathbb{R^{n \times n}}$ and $P$ is a permutation matrix. Let us take $\circ$ to be the element-wise product between two matrices. ...
1 vote
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### Hyperplane contains an inversible matrix

Let $H$ be an hyperplane of $M_n(\Bbb K)$ $(n\ge 2)$ Show that there exists $A \in M_n(\Bbb K)$ such that $H=\{M\mid \text{tr}(AM)=0\}$ Deduce that $H$ contains an invertible matrix
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### Find Matrix A such that $\operatorname*{argmin}_A ||H-A||^2_F + |A|_1$ from given matrix $H$

Question I have matrix $H$, I want to find Matrix $A$ such that: $$\operatorname*{argmin}_A ||H-A||^2_F + |A|_1$$ How can I do that? What's the rule of updating? Can someone please guide?
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### How to show the norm of the residual in GMRES minimization problem?

I couldn't quite catch the relationship between QR and it. What I'm confused about is what S and C mean, and how can I make desired proof? Let $e_i^{n}$be the i-th unit vector in $C^n$ The solution ...
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### Block matrices in MATLAB. [closed]

I am completely new to the matlab programming. Could please tell me algorithm/implementation of the block matrix M(PICTURE). How to code it in Matlab? Thank you.[This Block Matrix M ] Block Matrix ...
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### Remarquable identities $f(n) = \frac{a^n}{(a-b)(a-c)} + \frac{b^n}{(b-a)(b-c)} + \frac{c^n}{(c-a)(c-b)}$

Let $n$ be an integer, and \begin{equation} f(n) = \frac{a^n}{(a-b)(a-c)} + \frac{b^n}{(b-a)(b-c)} + \frac{c^n}{(c-a)(c-b)} \end{equation} \begin{equation} g(n) = \frac{(bc)^n}{(a-b)(a-c)} + \frac{(ac)...