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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2
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2answers
82 views
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Triangulation of matrices

Suppose that $A$ is some triangularizable matrix in $M_n(\mathbb R)$. The usual approach I know of to find a triangular matrix similar to it is to find bases for all the eigenspaces, then find their ...
4
votes
1answer
94 views
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Is Frobenius norm induced by 2 vector norms?

Let in the space $V$ defined norm $ ||\cdot||_V $ and in the space $W$ defined norm $ ||\cdot||_W $ Then consider operator norm induced by 2 vector norms $ ||\cdot||_V $ and $ ||\cdot||_W $ $ ||A|| ...
0
votes
1answer
42 views
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A problem with unitary matrices

Let $U$ be an $n \times n$ unitary matrix. And let $|\cdot |^2: \mathbb C^n \rightarrow \mathbb R_+^n$ be the function such that $|\mathbb w|^2$ is the vector which has its $i$-th entry equal to ...