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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4
votes
1answer
87 views
+50

Eigenvalues of block matrix of order $m+1$

How to find eigenvalues of following matrix? $\begin{bmatrix} mkI-A & -A & -A & \cdots & -A\\ -A & kI-A & O & \cdots & O\\ -A & O & kI-A & \cdots & O\\ ...
2
votes
1answer
40 views
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Block matrix of order $m$ with three block matrices

How to find eigenvalues of following block matrices? $M=\begin{bmatrix} A & B & O & O & O & O & O & \cdots & O & O\\ B & A & B & O & O & O ...
3
votes
2answers
39 views
+50

A is an antisymmetric matrix (of even size). B is another matrix such that $b_{i,j}=a_{i,j}+c$. Prove that |A|=|B|

I know that B would look something like this: $$\begin{bmatrix} c & a_{12}+c &...&&a_{1n}+c \\ -a_{12}+c & c &...&&a_{2n}+c \\ . \\ . \\ . \\ -a_{1n}+c & ...