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Results tagged with eigenvalues
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user 16807
Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, characteristic values (Hoffman and Kunze 1971), proper values, or latent roots (Marcus and Minc 1988, p. 144).
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Analytic formula for $\arg\max_{\|z\|_\infty \le 1}z^T A z$, where $A=uu^T+vv^T$
Let $u$ and $v$ be column vectors of size $n \gg 1$ (not both zero), and consider the matrix $A:=uu^T+vv^T$
Question
What is an analytic formula for $\arg\max_{\|z\|_\infty \le 1}z^TAz=\arg\max_{\|z …
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Analytic formula for leading eigenvector of $uu^T + vv^T$?
In this post https://math.stackexchange.com/a/112201/168758, the eigenvalues of $A$ were computed analytically.
Question
I wonder whether there is an analytic formula for the eigenvectors of $A$. … Observation
This answer https://math.stackexchange.com/a/112197/87355 shows how to compute the eigenvalues of $A$ via 2 iterations of Gram-schmidt. …
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Efficient computation of leading eigenvector of a matrix product of the form $ADA^T$, where ...
Let $A=[A_1|\ldots|A_m] \in \mathbb R^{n \times m}$ with $n \gg m \gg 1$ and $D=\text{diag}(d_1,\ldots,d_m)$ where $d_1,\ldots,d_m > 0$, and consider the $n\times n$ positive-definite matrix $X=\sum_{ …
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