# 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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### Minimum Elementary row/column transformations to find Inverse of given Matric

While working out some elementary transformation to find Inverse of matrix, it get in my mind, what is Minimum such transformations needed to find Inverse.
Consider the following flow on square matrices. $$Y(t)= \frac{d}{dt}X(t)$$ I would like to find a skew-Hermitian matrix $K$ which minimizes the following under the Frobenius norm. $$||[K,X]-Y||_F$$ We ...
Suppose I've got a nonsquare integer matrix, say $\begin{pmatrix}3 & 1 & 1 & 1\\1 & 1 & 1 &1\end{pmatrix}$ and want to compute its Smith normal form--in this case, \$\begin{...