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Results tagged with matrices
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user 32487
Questions where the notion matrix has an important or crucial role (for the latter, note the tag matrix-theory for potential use). Matrices appear in various parts of mathematics, and this tag is typically combined with other tags to make the general subject clear, such as an appropriate top-level tag ra.rings-and-algebras, co.combinatorics, etc. and other tags that might be applicable. There are also several more specialized tags concerning matrices.
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Sufficient conditions for invertibility of a block tridiagonal matrix
The following theorems generalize those in Tridiagonal matrices: inversion and conditioning
to all rational eigenvalues except $1, 1/2, 1/3$,
to complex eigenvalues,
to block-tridiagonal matrices. … In particular, this covers tridiagonal Toeplitz matrices. …
- 397
1
vote
Sufficient conditions for invertibility of a block tridiagonal matrix
Conditions for tridiagonal matrices
The following conditions are for tridiagonal matrices; i.e. $m_i = 1$ for each $i$. … In particular, this condition covers matrices which may not be strictly diagonally dominated. …
- 397
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Sufficient conditions for invertibility of a block tridiagonal matrix
This is in contrast to general block matrices which may require pivoting to complete an LDU-decomposition. … \end{aligned}$$
The minor of a product of matrices $X \in \mathbb{R}^{M \times N}$ and $Y \in \mathbb{R}^{N \times P}$ is:
$$\det((XY)_{I, J}) = \sum_{K \subset_{|I|}} \det(A_{I, K}) \det(B_{K, J}),$$ …
- 397