The relation between trace and determinant of a matrix
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 $M$?
Order of operations for multiplying three matrices
Jan 11, 2018 · Matrix multiplication is associative, so you can do it in whichever order you like. You can prove it by writing the matrix multiply in summation notation each way and seeing …
Singular vs. Non-singular - Mathematics Stack Exchange
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. …
Taking the inverse of a matrix is not a convex operation (or is it?)
Dec 31, 2025 · I was interested in the following statement that was discussed in this thread: Is taking the inverse of a matrix a convex operation? In short, this topic provides numerous …
Compute the characteristic equation of a $3 \times 3$ matrix
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 …
Differences Between Row Echelon and Reduced Row Echelon
Mar 29, 2016 · From Williams (source), pg. 348: The difference between a reduced echelon form and an echelon form is that the elements above and below a leading 1 are zero in a reduced …
Div and curl operators on matrix multiplied vectors
5 days ago · Let u (x) be a vector field of n dimensions and M (x) be a matrix of dimension mxn. Are there any elegant general identities for div and curl of : w(x)= M(x)u(x) Any identity i tried …
Let $A$ be an $n \\times n$ matrix that is both Hermitian and …
6 days ago · Let $A$ be an $n \times n$ matrix that is both Hermitian and unitary. Then, a) $A^2=I$ b) $A$ is real c) the eigenvalues of $A$ are $0$, $1$, $-1$ d) the minimal and …
Why Markov matrices always have 1 as an eigenvalue
Now in markov chain a steady state vector ( when effect multiplying or any kind of linear transformation on prob state matrix yield same vector) : qp=q where p is prob state transition …