1
vote
3answers
319 views

Checking for invertibility of large matrices in MAGMA

If you have a number of large matrices, and you wish to determine whether each matrix has determinant zero or not, what is the most efficient way to do this in MAGMA (it appears that calculating the ...
6
votes
1answer
1k views

Constructing a unitary matrix

Setting: Given a set of $n\times n$ matrices $A_i$, I would like to find a linear combination of these matrices $Q = \sum_i A_i x_i$ with $x_i$ a set of complex numbers, such that $Q$ is unitary: ...
1
vote
1answer
360 views

Efficient derivation of null space of large symbolic matrices?

Hi all, I'm wondering if anyone is aware of an efficient mechanism by which to derive the null space of a "large" symbolic matrix. Here, large means on the order of 10^2 rows, not necessarily ...
0
votes
2answers
105 views

Properties of adjacent submatrixes [closed]

Hi! I've encountered a matrix problem when designing an algorithm, which I cannot seem to figure out. I have a (square) matrix with the following properties: j<k → aij<aik, aji<aki ...
2
votes
4answers
2k views

Symmetrical Presentation of 4-Dimensional Rotation Matrix

This question is not urgent; just a matter of curiosity... It is relatively easy to generate an arbitrary 3D or even 4D rotation matrix using conjugation (i.e. YXY−1) of orthogonal rotations. I ...