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answered Prove that a small shift in the diagonal term leads to smaller spectral radius (for Perron-Frobenius theorem)
Feb
8
comment The formula $\DeclareMathOperator{tr}{tr}\mathrm{adj}(A)=\tfrac{1}{2}[(\tr A)^2-\tr(A^2)]I_3-[\tr A]A+A^2$ for the adjoint of a $3\times 3$ matrix
nice!!! ..........+1
Jan
20
answered Cholesky-type factorization of positive definite matrices
Jan
19
comment Proof relating inverse to determinant
This is really nice....I like it because it is self-contained. I believe a variant of proofs of Sherman-Morrison and Matrix-determinant lemma in fact use this kind of block matrix arguments.
Jan
19
answered Proof relating inverse to determinant
Jan
14
comment What is that thing that keeps showing in papers on different fields?
Really nice question!!.....
Jan
13
answered If all the eigenvalues of $A$ are distinct, then $B$ can be expressed uniquely as a polynomial in $A$ with degree no more than $n − 1$.
Jan
4
comment The significance of the composition of an operator and its adjoint
For an engineer, what you refer is the so-called Gramian Matrix. In signal processing, this often roughly equals the co-variance matrix which measures the inner-product between the signal vectors (columns of $T$). $\rho(A*A)$ corresponds to the largest possible scaling $A$ can impart on a unit-norm vector. In principal component analyis, Eigenvectors of the Gramian plays the role of the principal components.
Dec
28
comment How to reshape a nonlinear inquality into a linear matrix inequality?
Is it Schor or Schur?
Dec
28
revised How to reshape a nonlinear inquality into a linear matrix inequality?
edited tags
Dec
22
comment Is a symmetric matrix characterized by the diagonal of its resolvent?
really clever!!
Dec
22
answered Known Results on eigenvalues of $A$, $B$, $A+B$?
Dec
18
asked Known Results on eigenvalues of $A$, $B$, $A+B$?
Dec
18
comment Simultaneous diagonalization
diagonalize $AB$ perhaps?
Dec
18
answered How do I prove that the trace of a matrix to its $k$th power is equal to the sum of its eigenvalues raised to the $k$th power?
Dec
17
answered Quadratic form with Lagrange method
Dec
17
comment How to find the minimum distance from a point to a set?
can you add reference to the type of projection theorem you are referring to ?
Dec
15
revised An inequality related to matrix norm, inverse matrix
edited tags
Dec
4
revised Why does $A \circ {B^{ - 1}} + {A^{ - 1}} \circ B \ge 2{I_{n \times n}}$?
added 461 characters in body
Dec
4
comment Why does $A \circ {B^{ - 1}} + {A^{ - 1}} \circ B \ge 2{I_{n \times n}}$?
$x^H$ is the transpose conjugate of vector $x$. $xx^H$ is the outer product of column vector $x$ and row vector $x^H$. Can you ping me on email (username.at.gmail.com).