# Questions tagged [matrix]

Questions on the manipulation of matrices in Mathematica.

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### How do I construct a matrix using table command. I can not form it's function

I have to form a matrix like this. How ever I can not directly input. I have to form a function and then use the table command. I am stuck. {{2,5,10},{9,12,17},{28,31,36}}
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### How can I calculate the determinant of a 40$\times$40 symbolic matrix?

I tried to find the characteristic equation of the 40$\times$40 symbolic function by calculating its determinant in Mathematica. But Mathematica does not return me any output after long time ...
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### Implementation of quantum Uhlmann Fidelity in Mathematica

I want to implement the quantum Uhlmann fidelity $$F(\rho, \sigma) := \mathrm{tr} \left[\sqrt{\sqrt{\rho} \sigma \sqrt{\rho}} \right]^2.$$ in Mathematica as a measure of "closeness" between ...
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### What is the inverse Jacobian of a 4D model? [closed]

For a Jacobian Matrix where the elements are represented as J11 J12 J13 J14 J21 J22 J23 J24 J31 J32 J33 J34 J41 J42 J43 J44 what is the inverse jacobian of this Matrix?
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### How can I parallaize expresion that contains ParallelSum?

I have this code where the last part contains ParallelSum ...
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### Problem for defining continously Eigenvectors from Kane and Mele model

The model is a simple eigenvalue problem. A matrix that depends on some parameters kx, ky, t, defined by: ...
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### How to simplify the result of matrix according to the operation rules specified in the textbook?

We know that the inverse and transposition of composite matrices follow certain calculation rules. For example, $(ABC)^{-1}=(C^{-1})(B^{-1})(A^{-1})$, $(ABC)^T=C^TB^TA^T$, $ABC=E \Rightarrow BCA=E$. <...
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### Determine a negative semidefinite 5*5 matrix

I'd like to find the real parameters $\left\{p,\alpha ,a_{24},c_3,c_7,c_9,c_{10}\right\}$ in $M$, which is a $5\times 5$ real symmetric matrix, such that $M$ is negative semidefinite. My code for $M$: ...
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### Can the WishartMatrixDistribution command be used for generating random density matrices?

I am interested in generating random members of two classes of $n \times n$ positive-definite matrices $A$ and $B$--the former symmetric in nature, the latter, Hermitian. The standard (Ginibre-matrix-...
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### How to simplify a matrix with detailed steps?

When I simplify a matrix with a parameter, for example: (PS: it's the answer to the textbook) When I use RowReduce[] to simplify this matrix. it seems going too far to its simplest form: So, My ...
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### Determine a positive semidefinite 5*5 matrix

I'd like to find the real parameters $\left\{a_{14},c_6,c_8,c_{10},c_{12},c_{13},c_{14},c_{15},\alpha \right\}$ in M, which is a $5\times 5$ real symmetric matrix, such that M is positive semidefinite....
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### How can I use Compile to Evalaute a trace of a sympolic Matrix?

I would like to evaluate a trace of a matrix of size 4Wn×4Wn at different point (x,y). with <...
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### Getting a submatrix of a larger matrix [closed]

This should be straightforward, but the Mathematica documentation does not seem to help with this. Suppose I have a $10 \times 10$ matrix and want to get the $3 \times3$ submatrix define by the ...
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### Issues when applying list of indices to a matrix

I am interested in generating a 1D list of the upper-triangle elements of a matrix. I can grab the indices of these elements by doing: ...
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### Applying a function to every item in a column of a matrix

A problem that arises more often than I care for is that I want to modify specific elements nested lists. Examples may be wanting to add 1 to the second value, get ...
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### Determining Choices for Solution of a Matrix Equation Through NullSpace Function

I am trying to see how Mathematica chooses the basis vectors of the nullspace computed through: ...
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### How to use the function Resolve to verify this conclusion?

Let A be a non-zero square matrix of order n, $A^{*}$ be the adjugate matrix of A, and $A^{T}$ be the transposition matrix of <...
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### How to find some matrices that satisfy the constraints

I know that the three eigenvalues of the real third order matrix A are -1, 1, ...
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### what is the difference between two Eigenvalue[…] outputs

Can someone explain the difference between two types of Eigenvalue[...] operations: ...
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