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Results tagged with matrices
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user 119549
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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Conditions for $B$ that make $ADB + (ADB)^T$ positive (semi-)definite
At the end of the day, we have something like
$$
0 \leq x^TD_0W_0D_1W_1D_2 \dots W_ND_NCx
$$
With $D_i$ matrices that are all diagonal, square, positive, real matrices, and $W_i$ non-square real matrices … were a normal matrix, and had positive eigenvalues, then $WDC + (WDC)^T$ would also have positive eigenvalues (since $WDC$ would commute with it's transpose and the eigenvalues of the sum of commuting matrices …
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