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1d
reviewed Approve Inverse of partitioned matrices
1d
reviewed Leave Open Olympiad question on Pigeonhole principle
1d
reviewed Close Are $A$ and $A^\top$ similar?
1d
comment Producing lower bounds for $\text{trace}(A^2)$ for a positive semidefinite, symmetric matrix $A$
Related: Prove $\text{rank}(A)\ge\frac{(\text{tr}(A))^2}{\text{tr}(A^2)}$ when $A$ is Hermitian.
1d
comment Producing lower bounds for $\text{trace}(A^2)$ for a positive semidefinite, symmetric matrix $A$
Ha ha ha, this is great. +1
1d
answered Is this a circulant matrix?
1d
answered Producing lower bounds for $\text{trace}(A^2)$ for a positive semidefinite, symmetric matrix $A$
1d
comment Calculation of $trace(L^THL)$, L is lower triangular, H is symmetric.
I'm not sure if this is a practical method or not, but you may evaluate the trace probabilistically. If $x$ is a random vector whose entries are i.i.d. standard normal, then $\operatorname{trace}(A)=E(x^TAx)$.
1d
revised properties of the solution to a non-homogeneous matrix equation with a non-singular M-matrix
added 39 characters in body
1d
answered Mean value for $\tiny\left( \begin{array}{cc} X & X \\ -X & 1-X \\ \end{array} \right)$
1d
answered $A$ is a symmetric postivie definite matrix. Prove that $A^k$ is also a positive deinite
2d
answered For any $A, B \in SL(2, F)$, does knowing $\operatorname{tr}A$, $\operatorname{tr}B$, and $\operatorname{tr}AB$ specify $A$ and $B$?
Jul
27
answered Comparing $\text{tr}(A^{-1})$ and $\text{tr}(A(B+A)^{-2})$ for pd $A$ and psd $B$
Jul
26
comment real matrix with non-simple pure imaginary eigenvalue
Hmm, but the OP requires the eigenvalue to be non-simple, and yours are not.
Jul
25
comment Conditions for an orthogonal matrix equation
@curiousStudent Sorry, I mistakenly thought you meant $\mathbf A$ is block-diagonal. You mean the blocks themselves are diagonal? This is not always do-able (actually, it's usually not achievable).
Jul
25
comment Conditions for an orthogonal matrix equation
@curiousStudent In case both $B_1$ and $B_2$ are invertible (rather than merely $\mathbf B$ has full column rank), you may simply put $C=I,\ A_{11}=B_1^{-1},\ A_{22}=QB_2^{-1}$ and $A_{12}=A_{21}=0$.
Jul
25
answered Conditions for an orthogonal matrix equation
Jul
25
reviewed Leave Open Category theory,split idempotents,Set
Jul
25
reviewed Close limit of sequences with number of pairs
Jul
25
reviewed Leave Open Proof: $\mathbb{Z}[\zeta_6]$ is a PID.