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Questions about the properties of vector spaces and linear transformations, including linear systems in general.

2 votes

Invariants of Matrix Reordering

Singular values are definitely an invariant (because permutation matrices are orthogonal) but not a complete invariant! If you modify only the rows and columns order you do not modify the list of entr …
V. Delecroix's user avatar
4 votes

When is a matrix similar to a non-negative matrix?

If the column of $AU$ belongs (strictly) inside the space generated by the columns of $U$ then you have a dominant eigenvector inside $U$ (ie an eigenvector whose eigenvalue is real positive and of ma …
V. Delecroix's user avatar