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Results tagged with matrices
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user 75
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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Actions of the unit circle on finite complex matrices
So to sum up, actions of $S^1$ on $M_n(\mathbb{C})$ are naturally in bijection with traceless diagonalizable matrices $A$ whose eigenvalues are integers that are all equal mod $n$. … For $n=2$, such matrices $A$ have a particularly simple description: they are matrices with eigenvalues $k$ and $-k$ for some integer $k$. …
- 31.2k
3
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Is it that only with normal matrices, the transition matrix to its [del: inherent] [ins: own...
First, note that any diagonal matrix D is normal, since its adjoint is also diagonal and diagonal matrices commute. …
- 31.2k
20
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Linear transformation that preserves the determinant
Indeed, $T$ must preserve the rank $n$ matrices, and then the rank $n-1$ matrices are just the nonsingular locus in the variety of matrices with determinant $0$. … This implies $T$ preserves rank $n-1$ matrices. Rank $n-2$ matrices are then the nonsingular locus in rank $<n-1$ matrices so they are preserved, and so on. …
- 31.2k