Questions tagged [linear-algebra]

Linear algebra is concerned with vector spaces of all dimensions and linear transformations between them, including systems of linear equations, bases, dimensions, subspaces, matrices, determinants, traces, eigenvalues and eigenvectors, diagonalization, Jordan forms, etc. For questions specifically concerning matrices, use the (matrices) tag. For questions specifically concerning matrix equations, use the (matrix-equations) tag.

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Solution of coupled non-linear matrix difference equations encountered in calculating the determinat of a block partitioned matrix.

The determinant of the following $n N \times n N$ block partitioned complex symmetric matrix ($N \times N$ blocks) $$\begin{bmatrix}\mathbb{A} & \mathbb{B} &\cdots &\mathbb{B} \\ \mathbb{B}...
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Is the space of maps which satisfy this vanishing condition finite-dimensional?

Let $\mathbb{D}^n \subseteq \mathbb{R}^n$ be the closed $n$-dimensional unit ball. Let $h:\mathbb{D}^n \to \mathbb{R}^{k}$ be smooth, and suppose that $h(x) \neq 0$ a.e. on $\mathbb{D}^n$. Set $$V_h=\...
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Stable resolution of a $2\times2$ linear system

Cramer's method for the resolution of linear systems is known to be unstable, even in the $2\times2$ case. For general systems, stability can be improved by partial or full pivoting. When you ...