Jan 4, 2017 · Let $M$ be a symmetric $n \\times n$ matrix. Is there any equality or inequality that relates the trace and determinant of $M$?

Dec 23, 2025 · What is the size of the matrix whose SVD you want? If you know it a priori, what is the rank of your matrix whose SVD you want?

Feb 17, 2020 · A matrix/system of equations is singular is there are infinite solutions, but iff there is a unique solution then its non-singular? I haven't learned how to take a determinant yet. However, my …

May 1, 2025 · Coming up with the last eigenvalue should be easy if we use the fact that the trace of the matrix is the sum of the eigenvalues. The eigenvalues for this matrix are thus $\lambda_1 = 1, …

May 13, 2020 · The Hessian Simply, the Hessian is the matrix of second order mixed partials of a scalar field. $$\mathbf {H}_ {i, j}=\frac {\partial^ {2} f} {\partial x_ {i} \partial x_ {j}}$$ In summation: Gradient: …

Dec 18, 2025 · Say X ∈ Rn × d X ∈, with n ≫ d. If the (very) tall matrix X is centered, then the singular values of X are σi(X) = √λi(X), where the λi(X) are the eigenvalues of the covariance matrix X⊤X. …

Nov 17, 2017 · In fact, a quick check on Wolfram|Alpha shows that for a 2x2 matrix to be normalizable, the top left index must exactly equal the negative of the bottom right index (among other conditions) …

Oct 1, 2016 · One good reference is the Handbook Matrix Mathematics Theory, Facts and Formulas by Dennis S. Bernstein. Let $\mathbb {F}$ equal to $\mathbb {R}$ or $\mathbb {C}$.

For a lower triangular matrix, the inverse of itself should be easy to find because that's the idea of the LU decomposition, am I right? For many of the lower or upper triangular matrices, often I ...

Aug 9, 2020 · I have no clue on how this kind of matrices can be solved. Can anyone give a general strategy on how to solve matrices whose size are greater that $3\times 3$? That would be really helpful.