# Questions tagged [linear-algebra]

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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### Exploit bilinearity of KroneckerProduct symbolic calculations

Mathematica recognizes the bilinearity of the trace and the Kronecker product, as well as $Tr(A\otimes B)=Tr(A)Tr(B)$. But I have issues trying to implement this in symbolic calculations: Kronecker ...
81 views

### Determinant of 11x11 Matrix consumes immense amount of memory

I'm trying to take the determinant of an 11x11 matrix, constructed out of some functions I've defined ...
44 views

### Analytic calculation of the Pfaffian using sqrt

I'm trying to calculate the Pfaffian of a matrix. In general, it is given by, $$Pf(A) = \sqrt{\det(A)}.$$ In my case, $A$ is a matrix of $8\times8$. When I calculate the determinant of $A$, it yields ...
68 views

### How to show Timing command with more decimals?

I'm trying to compare the time that it takes to use the command LinearSolve when solving matrix(with random integers from 3 to 150 in each position) that are 10x10,20x20,30x30, ... , 150x150 for the ...
96 views

### Eigenvectors inside a maniupulate function

I am trying to make a physics application and it requires that the eigenvectors be taken for a 3x3 matrix. It is my intention that Mathematica never have to deal with the matrices symbolically. ...
113 views

### Fast computation of eigenvalues of large Hermitian matrices

I need to compute numerically all the eigenvalues of roughly $500$ large Hermitian matrices, $(5 \times 10^5) \times (5 \times 10^5)$). At best, I can speed up my computation such that it takes ...
22 views

### Doesn't print the Inverse of a Matrix [duplicate]

I want to calculate and print the inverse of a Matrix. But it calculates it but doesn't show the Output. What can be the problem here?
42 views

### Square root of a matrix with complex elements

How to compute the square root of the matrix Rho = {{Wxx, Wxy, Wxz}, {Wyx, Wyy, Wyz}, {Wzx, Wzy, Wzz}} if not all of its elements are real?
137 views

### Efficiently calculating matrix exponential of a recursively generated matrix

Given a matrix $A$ of size $N \times N$, I want to evaluate the function \begin{equation} F(t) = |\operatorname{Tr}(\exp(-i A t))|^2 \end{equation} as a function of $t$. Here, $A[n]$ is constructed ...
Suppose I have a bunch of vectors or matrices $v,v_1,v_2,\ldots, v_n$, living in an $N$ dimensional linear space. How to check (using mathematica) if $v$ is positively dependent on the set \$\{v_1,v_2,\...