1
vote
0answers
44 views

root of binary matrix

There is a square matrix A defined over the field GF(2). It means there are zeros and ones in its cells, xor stands for element summation, logical and - for multiplication. Is there any way to find ...
0
votes
1answer
38 views

Square root entries of matrices

How would you simplify something like this? $((\xi'\omega \xi)^{-1})^{0.5}$ where $\xi$ is a $k \times 1$ matrix, $\omega$ is a $k\times k$ square matrix. Thank you very much! Edit: Yes, though ...
5
votes
2answers
2k views

Find the roots of a polynomial using its companion matrix

I would like to find the roots of a polynomial using its companion matrix. The polynomial is ${p(x) = x^4-10x^2+9}$ The companion matrix $M$ is $M={\left[ \begin{array}{cccc} 0 & 0 & 0 ...
3
votes
2answers
617 views

roots of minimal and characteristic polynomial

Why is it, that for the matrix $A \in \text{Mat}(n\times n, \mathbb{C})$ the characteristic polynomial $\chi_A(t)$ and the minimal polynomial $\mu_A(t)$ have same roots? Since $\chi_A(t) = \mu_A(t) ...
3
votes
5answers
367 views

How to compute the characteristic polynomial of $A$

The matrix associated with $f$ is: $$ \left(\begin{array}{rrr} 3 & -1 & -1 \\ -1 & 3 & -1 \\ -1 & -1 & 3 \end{array}\right) . $$ First, I am going to find ...
2
votes
1answer
125 views

Finding the Zeros of a Matrix-Vector Equation

Here's another matrix algebra question, sorry if I'm coming at these incorrectly, but this kind of thing really isn't my forte :( Lets say we have the equation: $0 = -2 \mathbf{u}^{T} \mathbf{Z} ...