0
votes
0answers
52 views

Eigenvalue formula for 4x4 symmetric matrix

Is there a formula/algorithm that is accurate to used in finite precision arithmetic (aka numerical stable ) for small symmetric matrix of size 4x4. Additionally I'm looking if it require similar ...
1
vote
2answers
45 views

Computing an induced matrix norm

Assume I have a $n \times n$ matrix and a norm defined as $\|A\| = \max \limits_{x \not = 0}\frac{\|Ax\|}{\|x\|}$, where $\|x\| = \sqrt{\sum x_i^2}$. How can I compute this norm?
0
votes
1answer
168 views

Calculating eigenvectors and eigenvalues of a 2x2 complex matrix

I've previously asked elsewhere, http://stackoverflow.com/questions/21118820/non-trivial-eigenvectors-of-a-22-matrix-in-code, how to calculate the eigenvectors and eigenvalues of a 2x2 matrix in a ...
1
vote
0answers
341 views

Solving large, sparse system of linear equations

I have a system of linear equations as follows: $$(A+I)x=B$$ where $I$ is the $n\times n$ identity matrix, $A$ is a $n\times n$ matrix such that the first and last rows are blank, and, for every ...
3
votes
0answers
47 views

Supremum over unitary group action

Let $A$ and $B$ are two given Hermitian operators on matrix algebra $M_n(\mathbb{C})$. $A$ is positive semi-definite with unit trace. I want to know the general method for calculating the following ...
1
vote
1answer
65 views

Is there a good strategy for computing eigenspace corresponding to $1$ of a matrix with entries of trigonom

For example, say $A= \left ( \begin{matrix} \cos x & -\sin x & 0 \\ \cos y \sin x & \cos x \cos y & -\sin y \\ \sin x \sin y & \sin y \cos x & \cos y \end{matrix} \right)$. ...
-2
votes
2answers
78 views

Is there any good strategy for computing null space of a matrix with entries $\cos x$ and $\sin x$?

For example, say $A= \left ( \begin{matrix} \cos x & -\sin x & 0 \\ \cos y \sin x & \cos x \cos y & -\sin y \\ \sin x \sin y & \sin y \cos x & \cos y \end{matrix} \right)$. ...
2
votes
0answers
33 views

Computing a particular finite set of quaternion matrices.

Let $B = \left(\frac{-1,-11}{\mathbb{Q}}\right)$ be a choice of quaternion algebra ramifying at $11$ and consider the maximal order ...
1
vote
2answers
159 views

Space spanned by matrices

I have a set of 5 by 5 matrices, M1,M2,...,M19 ,M20. I want to try to find a basis from this set and also to find relationships between these matrices. This is how I think I should approach the ...
1
vote
1answer
56 views

Matrix completion: supplementary questions

Continuation of the question here, what is going to happen if we change the some of the conditions. I write it as a quote from here and change the appropriate places which are underlined: I need ...
1
vote
1answer
121 views

Matrix completion

I need to find an algorithm (if exists) of the following matrix completion problem. I need to construct $n^2$ positive semi-definite matrices, say $\{P_i\}_{i=1}^n$. Entries of these matrices are ...
0
votes
0answers
162 views

Solving an overdetermined system of inequalities using null-space arguments

The solutions to a linear system of equations: $$A\cdot x = b$$ (where $x$ is a $(n\times 1)$ column vector, $b$ is a $(m\times 1)$ column vector and $A$ is $(m\times n)$ matrix) can all be ...
2
votes
1answer
222 views

Given two sets of vectors, how do I find a change of basis that will convert one set to another?

Given two sets of dimension $n$ vectors $\lbrace v_1 , v_2 , \ldots , v_m \rbrace$, $\lbrace u_1, u_2, \ldots , u_m \rbrace$, where $m > n$, is there a computational method (in particular, using ...
1
vote
0answers
147 views

Calculation of stopping condition for Conjugate Gradient

I am a person with programming background and need some math help. I am looking at the source code for an implementation of the Conjugate Gradient iterative solver ...
0
votes
1answer
117 views

more matrix inversion

Related to a previous question: Suppose I want to invert a (sparse) matrix written in block form as \begin{array}{cccc} A_{11} & A_{12} & \ldots & A_{1n}\\ A_{21} & A_{22} & & ...
0
votes
2answers
130 views

efficient matrix inversion problem

So I'm trying to invert a matrix of the $\begin{pmatrix} A & B \\ C & D \end{pmatrix}$ where $A$ and $D$ are square, $D$ is much larger than $A$, and $D$ is diagonal. $A$ $B$ and $C$ have no ...