Prove $A>P^TB^-1P$ iff $B>PA^-1P^T$. The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Given two symmetric, real, positive definite matrices, $A,B$ such that $AB=BA$, prove that $AB$ is positive definite.Prove that matrix is symmetric and positive definite given the fact that $A+iB$ is.prove exists $hat E$ defined on the set $Sym^+(Bbb R^3)$ of symmetric positive definite matrices, such that $E(F)=hat E(F^TF)$?Polar decomposition of real matricesWhat can we say about the polar decomposition of a skew symmetric matrix?Nearest Symmetric MatrixQuestion involving orthogonal matrix and congruent matrices $P^tAP=I$For a positive definite symmetric matrix, the orthogonal diagonalization is a SVD of A.Does polar decomposition give commutative answer, i.e. it is group isomorphism?Singular Values of Symmetric Matrix
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Prove $A>P^TB^-1P$ iff $B>PA^-1P^T$.
The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Given two symmetric, real, positive definite matrices, $A,B$ such that $AB=BA$, prove that $AB$ is positive definite.Prove that matrix is symmetric and positive definite given the fact that $A+iB$ is.prove exists $hat E$ defined on the set $Sym^+(Bbb R^3)$ of symmetric positive definite matrices, such that $E(F)=hat E(F^TF)$?Polar decomposition of real matricesWhat can we say about the polar decomposition of a skew symmetric matrix?Nearest Symmetric MatrixQuestion involving orthogonal matrix and congruent matrices $P^tAP=I$For a positive definite symmetric matrix, the orthogonal diagonalization is a SVD of A.Does polar decomposition give commutative answer, i.e. it is group isomorphism?Singular Values of Symmetric Matrix
$begingroup$
Suppose $A,B$ are $ntimes n$ positive definite real symmetric matrices,P is an $ntimes n$ real matrix, prove that
$A>P^TB^-1P$ iff $B>PA^-1P^T$.
By using the orthogonal diagonalization, I can prove this when $P$ is nonsingular. I have tried Polar decomposition, but I didn't know how to deal with $P$, since it can be singular.
linear-algebra matrices matrix-decomposition
asked Mar 25 at 9:28
Tao XTao X
1016
$endgroup$
add a comment |
$begingroup$
Suppose $A,B$ are $ntimes n$ positive definite real symmetric matrices,P is an $ntimes n$ real matrix, prove that
$A>P^TB^-1P$ iff $B>PA^-1P^T$.
By using the orthogonal diagonalization, I can prove this when $P$ is nonsingular. I have tried Polar decomposition, but I didn't know how to deal with $P$, since it can be singular.
linear-algebra matrices matrix-decomposition
asked Mar 25 at 9:28
Tao XTao X
1016
$endgroup$
add a comment |
$begingroup$
Suppose $A,B$ are $ntimes n$ positive definite real symmetric matrices,P is an $ntimes n$ real matrix, prove that
$A>P^TB^-1P$ iff $B>PA^-1P^T$.
By using the orthogonal diagonalization, I can prove this when $P$ is nonsingular. I have tried Polar decomposition, but I didn't know how to deal with $P$, since it can be singular.
linear-algebra matrices matrix-decomposition
asked Mar 25 at 9:28
Tao XTao X
1016
$endgroup$
Suppose $A,B$ are $ntimes n$ positive definite real symmetric matrices,P is an $ntimes n$ real matrix, prove that
$A>P^TB^-1P$ iff $B>PA^-1P^T$.
By using the orthogonal diagonalization, I can prove this when $P$ is nonsingular. I have tried Polar decomposition, but I didn't know how to deal with $P$, since it can be singular.
linear-algebra matrices matrix-decomposition
linear-algebra matrices matrix-decomposition
asked Mar 25 at 9:28
Tao XTao X
1016
asked Mar 25 at 9:28
Tao XTao X
1016
asked Mar 25 at 9:28
Tao XTao X
1016
asked Mar 25 at 9:28
Tao XTao X
1016
asked Mar 25 at 9:28
Tao XTao X
1016
1016
add a comment |
add a comment |
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