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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5
votes
2answers
141 views
+50

Kernel of a Vandermonde like matrix

I am wondering how to show that the following matrix has trivial kernel: $$\begin{bmatrix} 1&1&1&1&1&1 \\ s_1&s_2&s_3&s_4&s_5&s_6 \\ ...
5
votes
1answer
82 views
+50

Eigenvalue of block matrix of order $2n$

How to find eigenvalues of following block matrix? $$P=\begin{bmatrix} A & B \\ B & A \end{bmatrix}$$ Where, $A=\begin{bmatrix} 0 & 1 & 0 & 0 & 0 & 0 & \cdots & ...
3
votes
0answers
91 views
+50

Multiplication of unitary matrices to make symmetric off-diagonal elements zero

Context Starting with a unitary matrix $U$ of size $m \times m$, I have read of a way to obtain a diagonal matrix by sequentially multiplying $U$ from the right by unitary matrices $V$ of a certain ...