What is the proof of the fact "a positive definite matrix has a unique positive definite square root"?
67686
Square root of Positive Definite Matrix
135171
Under what conditions is the difference between a rank $1$, postive semidefinite matrix and a hermitian matrix positive semidefinite?
110271
Given a matrix with non-negative real entries, can you algebraically prove that it has a non-negative eigenvalue?
30268
Positive definite matrix must be Hermitian
158205
If $A+A^T$ is negative definite, then the eigenvalues of $A$ have negative real parts?
109167
Nth roots of square matrices
116136
Proof that the inverse of a square matrix is unique
54211
If $A$ and $B$ are positive definite, then is $B^{-1} - A^{-1}$ positive semidefinite?
56818
Prove that if $A$ is positive, then $\exists\;\alpha>0$ such that $\langle Ax, x \rangle\geq \alpha|x|^2$ for $x\in\Bbb{R}^n$
117175
Proof that the 2-norm of orthogonal transformation of a matrix is invariant
38945
On the proof that the product of diagonal matrices is a diagonal matrix?
73807
Prove positive definiteness
76110
Proving that the zero vector is unique
97204
Is there a unique solution for this quadratic matrix equation?
86623
Why is $B^TB+\lambda\Omega$ positive definite?
12868
Is the product of symmetric positive semidefinite matrices positive definite?
115296
Under what conditions does a matrix $A$ have a square root?