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Results tagged with matrices
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user 7311
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.
17
votes
Can we add two matrices by performing an operation on their eigenvalues & eigenvectors?
Consider a diagonal matrix A that has eigenvaues 1 and -1 with eigenvectors $e_1$ and $e_2$. Then A and -A have the same eigenvalues and eigenvectors as A and A. But A + -A = 0 and A + A $\ne$ 0
- 15.3k
12
votes
5
answers
2k
views
Is this formulation of the Singular Value Decomposition standard?
Gil Strang's textbooks) it is always stated in terms of writing an
$m \times n$ matrix $M$ (say of rank $r$) as a product $U \Lambda V$, where $U$ and $V$ are
orthogonal $m \times m$ and $n \times n$ matrices … I certainly realize that this is a pretty obvious reformulation of SVD, once you see it (and
those poor misguided souls who prefer matrices to linear transformations may even see it as
a step backwards …
- 15.3k
0
votes
Irreducibility of determinant of symmetric matrix
I think you must mean the characteristic polynomial (the determinant is a scalar, not a polynomial), but then what about the identity matrix---it has characteristic polynomial $(\lambda-1)^n$ and so i …
- 15.3k