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
143 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
85 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
94 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 ...
16
votes
1answer
301 views
+50

What is the number of $n \times n$ binary matrices $A$ such that $\det(A) = \text{perm}(A)$?

Recall that the permanent is the 'positive analog' of the determinant whereby the signs in the cofactor expansion process are taken as positive. That is, the permanent is the immanant corresponding to ...