Questions about Mathematica functionality related to manipulating vector spaces and linear mappings between such spaces. This includes determination of matrix properties, matrix transformations, decompositions, and factoring.

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2
votes
1answer
295 views

Sort eigenvectors of a list of matrices

I have a list of matrices and want to obtain a list of eigenvectors and eigenvalues for each matrix, both sorted by the size of the eigenvalue. If I write ...
2
votes
0answers
167 views

(Symbolic) LinearSolve is slower/different after upgrading to Mathematica 9

Yesterday I upgraded from mathematica 8.0.4.0 to 9.0.1.0. Trying to run the same notebook I used many times before, it takes ages to evaluate a symbolic (linearsolve) expression which before was ...
2
votes
1answer
143 views

Why `FindMaximum` doesn't work in my example

Consider the following function ...
2
votes
2answers
389 views

Logarithm of a matrix in base 2?

Mathematica provides the built-in command MatrixLog, which operates on a square nonsingular matrix, but it returns the natural logarithm. How can I find the base 2 ...
1
vote
0answers
79 views

Mathematica program for PLUR decomposition of a symbolic matrix using full pivoting

I wanted to ask if there is a Mathematica program for PLUR decomposition of a symbolic matrix M, such that M = P*L*U*R, using FULL (row and column) pivoting, and where R = reduced row echelon form of ...
1
vote
2answers
144 views

Are variables always assumed to be real in Jordan Decomposition?

If you give the following input in Mathematica 9.0 (Student Edition): JordanDecomposition /@ ({{1, #}, {#, -1}} & /@ {i, I}) Mathematica gives you two ...
1
vote
1answer
101 views

Efficient calculation of diagonal matrix elements

I have a matrix $V$ of size $M$ in which each row $i$ is a vector $v_i$. Now I have another matrix $H$ and I would like to calculate as efficiently as possible the list of values $v_i^\dagger\cdot H\...
1
vote
1answer
204 views

Transform linear system into a matrix form

I have a system of linear equations in variables $A_n$ of form: $$ \sum _{k=-K}^K h_k A_{n-k} J_{n-k}\left(\frac{(1-i) \text{$\eta $Sqrt}(n-k)}{\sqrt{2}}\right)+A_n\left(\frac{(1-i) \eta \sqrt{n-...
1
vote
1answer
250 views

What is most efficient way to convert system of equations to collection of functions?

I have the type of system M.x = b, where M is a known matrix and b is a known vector. M contains many parameters, call the entire parameter set 'a', so M => M[a]. I want to be able to efficiently ...
1
vote
2answers
2k views

How to Solve or LinearSolve $A = I$ matrix equation?

I'd like to solve this equation for $A = B$ where $B = I$, which represents 3 systems of 3 linear equations, for $a, b, c, d, e, f$, without writing LinearSolve 3 ...
1
vote
2answers
146 views

How to extend “List-of-numbers-with-number” arithmetic to “List-of-X-with-X” arithmetic? [duplicate]

I'll start with a couple of examples (since this is all one can get from the documentation anyway). First, adding lists of numbers equal length is done term-by-term. E.g. ...
1
vote
1answer
284 views

Efficient algorithm to generate a basis for exact diagonalization

The problem is described as follows: I need to generate a basis(matrix) in lexicographic order. For two different basis vector $\{n_1,n_2,\cdots,n_M\}$ and $\{t_1,t_2,\cdots,t_M\}$, there must exist ...
1
vote
0answers
154 views

Request for clarification of Eigensystem::eivn message

What causes the problem of "two eigenvectors associated to one single multiplicity eigenvalue" that I am experiencing? After several transformations to simplify an unwieldy matrix, I end up with the ...
1
vote
0answers
79 views

CharacteristicPolynomial returns 0

I have a following matrix. ...
0
votes
1answer
151 views

Mathematica Lattice Reduce Command

I'm going through a very old copy of "Mathematica: A System for Doing Mathematics by Computer" for self practice. I'm on chapter 3, and ran into the LatticeReduce ...
0
votes
0answers
173 views

Mathematica function Det has unexpected behavior

I am using Mathematica "Kernel" -> {"Version" -> "9.0 for Microsoft Windows (64-bit) (January 25, 2013)", "ReleaseID" -> "9.0.1.0 (4055652, 4055188)" on a Win 7 machine. The file listed below uses ...