Prove that if the quadratic form $x^{T}Ax$ is positive definite, so is $x^{T}A^{-1}x$
133149
Inverse of a Positive Definite
101861
How do you prove that $tr(B^{T} A )$ is a inner product?
154327
$A^2X = X$ show that $AX = X$, if $A_{ij} > 0$ and $x_{i} > 0$
7457
Prove that $J^+AJ$ has positive eigenvalues
67820
Showing that $(A_{ij})=\left(\frac1{1+x_i+x_j}\right)$ is positive semidefinite
55377
Non-zero eigenvalues of $AA^T$ and $A^TA$
119032
Is ${\bf x^TAx} \ge { a \bf x^Tx}$ for some $a>0$ not dependent on $\bf x$ if $\bf A$ is positive definite matrix?
34702
Show $|A + uv^T| = (1 + v^T A^{-1} u) |A|$
3038
For positive invertible operators $C\leq T$ on a Hilbert space, does it follow that $T^{-1}\leq C^{-1}$?
69349
If $A$ is positive definite, then $\int_{\mathbb{R}^n}\mathrm{e}^{-\langle Ax,x\rangle}\text{d}x=\left|\det\left({\pi}^{-1}A\right)\right|^{-1/2}$
86623
Why is $B^TB+\lambda\Omega$ positive definite?
145125
How to prove that $A^{-1} + B^{-1}$ is invertible given the conditions
11911
How to prove the positive definite property of the semidefinite matrix with regularization?
23095
Prove that T is a linear transformation
98298
Prove that bilinear form can be presented as product of linear forms if and only if it has rank one
37985
Show that $|x|^2 = |y|^2$ with $A$ orthogonal and $Ax = \cos (θ)x − \sin (θ)y$, $Ay = \sin (θ)x + \cos (θ) y$
39082
Proving $x^\alpha-\alpha x \le 1- \alpha $