Prof Douglas Arnold's Group tag:blog.lib.umn.edu,2011-03-09:/lixx1445/myblog//13624 2011-03-10T00:33:09Z Movable Type Enterprise 4.31-en relation between different definitions of maximal nonnegativity tag:blog.lib.umn.edu,2011:/lixx1445/myblog//13624.279542 2011-03-10T00:33:09Z 2011-03-10T00:33:09Z Let $A\in R^{m\times m}$ be a symmetric matrix and $N$ a subspace of $R^m$. Proof or disprove: The following are equivalent: 1) $x^T A x \ge 0$ for all $x\in N$ and $\dim N$ is equal to the number of... arnold http://blog.lib.umn.edu/cgi-bin/mt-cp.cgi?__mode=view&blog_id=13624&id=29229 Let $A\in R^{m\times m}$ be a symmetric matrix and $N$ a subspace of $R^m$.
Proof or disprove:

The following are equivalent:

1) $x^T A x \ge 0$ for all $x\in N$ and $\dim N$ is equal to the number of nonnegative
eigenvalues of $A$.

2) There exists a matrix $M\in R^{m\times m}$ such that $x^T M x \ge 0$ for all
$x\in R^m$, $ker(A-M)+ker(A+M)=R^m$, and $N=ker(A-M).

]]> How-to tag:blog.lib.umn.edu,2011:/lixx1445/myblog//13624.279527 2011-03-09T22:56:36Z 2011-03-09T23:31:28Z To add simple content, just use "Start Topic". To add more complicated content (with file uploads for example), login to uthink, choose this blog and Write entries. Inline math: \$\int_a^b f(x) dx=0\$ gives: $\int_a^b f(x) dx=0$ Display math: \$\$ H^i(X;G)\times... lixx1445 http://blog.lib.umn.edu/cgi-bin/mt-cp.cgi?__mode=view&blog_id=13624&id=29222 To add simple content, just use "Start Topic".
To add more complicated content (with file uploads for example), login to uthink, choose this blog and Write entries.

Inline math:
\$\int_a^b f(x) dx=0\$
gives:
$\int_a^b f(x) dx=0$

Display math:
\$\$
H^i(X;G)\times H^j(Y;G) \longrightarrow H^{i+j}(X\times Y;G)
\$\$
gives:
$$
H^i(X;G)\times H^j(Y;G) \longrightarrow H^{i+j}(X\times Y;G)
$$

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