# Tagged Questions

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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### Comparing Bases in $\mathbb{R}^{n}$

A bit of trouble with the following question: Let $\mathcal{B}$ be the basis of $\mathbb{R}^{n}$ consisting of the vectors $\vec{v_1},\vec{v_2},\cdots,\vec{v_n}$, and let $\mathcal{E}$ be some other ...
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### Square root-related calculations with matrices

If $\mathbf A$ is an $n \times n$ matrix such that $\mathbf A^6 = \mathbf I_n$ (the identity matrix), is it true that either $\mathbf A^3 = \mathbf I_n$ or $\mathbf A^3 = \mathbf -I_n$? I'm ...
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### Equivalence proofs concerning matrices and systems of linear equations

Let $\mathbf A$ be the augmented $m × (n + 1)$ matrix of a system of $m$ linear equations with $n$ unknowns. Let $\mathbf B$ be the $m × n$ matrix obtained from $\mathbf A$ by removing the last ...