# Tagged Questions

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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### Is this problem parametrically solvable or it can just be solved for specific $\sigma$ and $\theta$?

In order to solve This problem: What is the maximum value of coefficient fv with the constraint that the matrix is positive semi-definite?, I have used the following code (Determinant is computed by ...
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### Array Flattening arrays of matrices given by rules

Fix an $n$ and an $m$ positive integers.I have some set of four $n\times n$ matrices $A$,$B$,$Y$,$Z$ (where $Z$ is the zero matrix). I'd like to input the $nm\times nm$ matrix of block matrices given ...
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### Generation of Space Representation of non-crystallographic Point Groups

In Mathematica the command FiniteGroupData[{"CrystallographicPointGroup",<group number>}, "SpaceRepresentation"] yields the space representation ...
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### Incorrect Left and Right Eigenvectors in Mathematica

I'm trying to find the Left and Right Eigenvectors of a pretty straightforward matrix, but Mathematica doesn't seem to be able to do it for even a 200 dimensional matrix. Background: Given an ...
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### non negative matrix factorisation [closed]

i am working on a project involving the use of non negative matrix (NMF) for the separation of a mixture of audio signals.can please give me the mathematical explanation of NMF so that i can ...
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### Orthonormalization of non-hermitian matrix eigenvectors

When using Orthogonalize[] one can specify which definition of "inner product" is to be used. For example, ...
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### How do I disable that Mathematica orders terms in lexicographic order?

I have matrices with entries where the order of the entries is important. Unfortunately Mathematica resorts terms in products in a lexicographic order. For example, ...
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### Rewriting List of Matrix Equation in Terms of Individual Equations? [duplicate]

I have a list of matrix equations M1={{a1,b1},{c1,d1}}; A1={{x1,y1},{z1,w1}}; M2={{a2,b2},{c2,d2}}; A2={{x2,y2},{z2,w2}}; sys={M1==A1,M2==A2}; which I would like ...
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### Optimizing over every element in a vector [closed]

So I have a 16 element vector, called LUEigenvector, depending on a series of variables a1,a2,...b1,b2...c1,c2... All the elements depend on all the variables. I want to use NMinimize sequentially, ...
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### Computing the logarithmic spectral norm rapidly

I wish to compute the logarithmic spectral norm of a square matrix $A$, which is defined by $$\mu_2[A]=\lim_{t\downarrow0}\frac{\|I+tA\|_2-1}{t}.$$ Hence, I simply code ...
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### What is the fastest way to obtain the eigenvalues of a Wishart matrix?

I would like a fast method of creating a sample of random numbers which corresponds to the eigenvalues of a Wishart matrix: For M>N the eigenvalues \lambda_i are given by the jpd Where $K_N$ is ...
43 views

### Solving simultaneous and determinant given constant value and variable T (temperature) [closed]

How to solve this two simultaneous equations? these two equations got from this free energy equation ...
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### CharacteristicPolynomial returns 0

I have a following matrix. ...
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### Eigenvalues are not the same in the special case

I have this matrix: h = { {e1, 2, x}, {2, 2, x}, {x, x, 2} }; I want to calculate the eigenvalues and then set x equal to zero: ...
133 views

### What is the correct way to perform the Gram-Schmidt process?

Im trying to do a simple processing in Mathematica. My original code was in Matlab. Part of the computation is Gram-Schmidt process, which is an iterative calculation. Every vector is changed ...
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### How can I calculate $(y - A \,x)^{T}(y -A\,x)$ symbolically? [closed]

Given that $x$ and $y$ are column vectors and $A$ is a matrix, I figured out the result $y^{T}y-2y^{T}Ax +x^{T}A^{T}A\,x$ I want to use Mathematica to make such calculations. how do I enter them into ...
276 views

### How to know the usage of undocumented function like LinearAlgebraBLAS?

BLAS is not documented in mathematica. Using ?LinearAlgebraBLAS* gives But None of the function has a detailed usage information Click any of the ...
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### Reliably computing the signature of a matrix with small eigenvalues

When asked to compute the eigenvalues of the following matrix ...
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### Nonrectangular tensor encountered [closed]

I am trying to solve a system of equations which characteristic matrix: ...
187 views

### Pack Solve results into a vector

I am currently using a really easy function to get the eigenvectors of a corresponding eigenspace: ...
66 views

### How to solve lowest eigenvalue with Lanczos or Arnoldi algorithm? [closed]

By setting Method->Arnoldi in Eigensystem I was able to solve lowest eigenvalue and eigenstate of a large sparse matrix. ...
99 views

### Hermitian Matrix

From Derbyshire's Prime Obsession, I would like to get the Mathematica code to generate a Hermitian matrix for evaluation and display. $256 \times 256$ would be nice. Random Normal distribution, ...
144 views

### strange timing result of LinearAlgebraBLAS in mathematica? [closed]

BLAS is short for "Basic Linear Algebra Subprograms". It is a famous collection of routines for doing linear algebra. I just know from Oleksandr R. that mma can directly call BLAS under the context ...
91 views

### Finding matrix given null space

Suppose I input a very large $n$ integer vectors and I wish to compute the matrix whose nullspace is spanned uniquely by these vectors. Is there an appropriate command/module to do this using ...
123 views

### How to be more efficient/faster with this MatrixExp-vector multiplication?

I am looking for expertise that helps to improve speed of the code below. First, a little bit of background: There is some system of differential equations $\dot{\vec{m}}(t)=S(t)\vec{m}(t)$. In order ...
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### Minimization of linear combination of vectors

Suppose I have a vectors in $\mathbb{R}^{6}$. For example, take the vector $v = k(-2,2,4,6,2,2)$. I would like to find some $k$ with the constraint that the last two components are necessarily ...
3k views

With some matrices, I am receiving the following message: ...
I'm trying to improve efficiency of my code in which main task is a solution to huge (~$10^4\times 10^4$) but sparse linear system $$Ax=b$$ (In fact my aim is to solve nonlinear equations $F(x)=0$, ...
How can I use Map over two indices with a condition? I am trying to calculate second derivative of an eigenvalue, $\lambda_i(x)$, of $n \times n$ matrix $M(x)$ ...