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Results tagged with linear-algebra
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user 30364
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
56
votes
real symmetric matrix has real eigenvalues - elementary proof
How about Jacobi's proof?
See, e.g., Folkmar Bornemann, ``Teacher's Corner - kurze Beweise mit
langer Wirkung,'' DMV-Mitteilungen 3-2002, Seite 55 (in German, sorry). Sorry, I don't have the original …
- 5,309
3
votes
Accepted
Schur complement and negative definite matrices
This should be a comment, but I can not yet post comments.
You got Schur's complement lemma wrong, the matrix
$$\left(\begin{array}{cc} 1 & 1 \newline 1 & -1 \end{array}\right)$$
satisfies you condit …
- 2,201