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Results tagged with matrices
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user 141969
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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Two versions of Sylvester identity
MathWorld presents the following two versions of Sylvester's determinant identity, relating to an $n\times n$ matrix $\mathbb{A}$:
First:
$$
|\mathbb{A}||A_{r\,s,p\,q}| = |A_{r,p}||A_{s,q}| - |A_{r,q} …
- 419
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Linear independence of vectors in Graph Theory
This implies that the two matrices, when joined to create an $n$ by $n$ matrix, create a single REGULAR (non-singular) matrix - no problem there. …
- 419
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Co-trees of a simple graph
Consider fundamental cycles (say $k$ of them) of a specific spanning tree of a simple graph (with $m$ edges) which is also connected and has no one-edge bonds.
Make the graph directed (in an arbitrary …
- 419
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Co-trees of a simple graph
This implies that (integer-valued) determinants of each of the RHS matrices have the same property (being equal to $1$ or $-1$). …
- 419