Tagged Questions

For any topic related to matrices. This includes: systems of linear equations, eigenvalues and eigenvectors (diagonalization, triangularization), determinant, trace, characteristic polynomial, adjugate, transpose, Jordan normal form, matrix algorithms (e.g. LU, Gauss elimination, SVD, QR), ...

15 views

39 views

16 views

Reducing a rectangular matrix of large rationals to small rationals

I have a large matrix (~1000 by ~2000), whose entries are purely rational numbers, typically involving large fractions, that is numbers (much) larger than 10^8 in denominator/numerator. The original ...
107 views

Are there singular matrices such that if we change any entry it will be non-singular?

Prove or disprove: for each natural $n$ there exists an $n \times n$ matrix with real entries such that its determinant is zero, but if one changes any single entry one gets a matrix with non-zero ...
166 views

If A and B are diagonalizable then so is AB

When we have to n×n matrices that can be made diagonal (maybe not in the same basis), is it true that the same works for their product?
53 views

Find the matrix representation

The question I'm stuck on asks: Find the matrix representation of the differential operator D acting on the space of polynomials of degree at most $3$ with basis $(3, 1 + x, x − x^ 2 , 1 + x^ 3)$, ...
18 views

Eigenvector with matrix amlost full with zeros

Hi i have weird problem with calculate eigenvector from simplest matrices. So have something like this: $A = \begin{bmatrix} \frac{1}{2} & 0 \\ 2 & \frac{1}{2} \end{bmatrix}$ Eigenvalues are ...
54 views

Maximum 2x2 squares in given rectangle

I have a matrix of size nxm which consists of 0s and 1s..so i have to place 2x2 squares in matrix where there is 0. You cant place square where 1 is present. The question is maximum 2x2 squares that ...
23 views

non-singular matrix block matrix over $\mathbb{Z}_p$

Let $p$ be a prime number and $A,B,C\in M_n(\mathbb{Z}_p)$ be nonsingular circulant matrices. How can I prove that this matrix $$\begin{bmatrix} A &B\\ B &C \end{bmatrix}$$ is nonsingular? I ...
62 views

Find “almost inverse” of positive definite bilinear form

Let $A$ be a positive definite $d \times d$ matrix, and define $A(x,x)=x^TAx$. Let $x$ be a point such that $\vert x^T\xi\vert^2\leq \xi^T A\xi$ for all $\xi\in\mathbb{R}^d$. Is this somehow ...