# Tagged Questions

Questions on the manipulation of matrices in Mathematica.

133 views

### Need Help Writing (a Pascal) Matrix in Mathematica

I want to write a function $f[n]$ in Mathematica which gives me an $n\times n$ lower triangular Pascal matrix with a row of zeros in between each nonzero row. That is, I want the matrices ...
243 views

### A dot appearing after a zero, and making the entries of a matrix into fractions

For more info about the difference between 0. and 0 I am a self-taught Mathematica user and I have some elementary questions-- perhaps too elementary for this site, but here they are. If ...
386 views

### stationary distribution of a transition matrix

How can I solve the stationary distribution of a finite Markov Chain? In other words, how can I estimate the eigenvectors of a transition matrix?
88 views

### Matrix multiplication that includes a tensor

How would I best express the following in Mathematica: $\begin{pmatrix}2 & 4\end{pmatrix} \begin{pmatrix}r_1 & r_2\\r_3 & r_4\end{pmatrix} \begin{pmatrix}6 \\ 8\end{pmatrix}$, where $r_i$ ...
569 views

### How to substitute numeric values in a symbolic Jacobian matrix?

I have a multi-variate function from $\mathbb{R}^n\to\mathbb{R}^n$. Choosing any desired initial vector, we can produce the corresponding function value, which is a vector as follows. The main problem ...
63 views

### Defining an Implies operation that works for Boolean matrices

I have two Boolean matrices, that both have dimensions m x n. I want to create a function TableImplies, which would return True ...
229 views

### Efficient method for inverting a block tridiagonal matrix

Is there a better method to invert a large block tridiagonal Hermitian block matrix, other than treating it as a ordinary matrix? For example: ...
304 views

### TensorContract of inverse matrix

Matrix inverse in mathematica If $A$ is an invertible $n \times n$ matrix, then $A\cdot A^{-1} = I$. To get this statement in Mathematica, you need the assumption ...
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### Efficiently finding the maximum value of a column in a matrix

Imagine I have a matrix of the following form: TestArray = $((a_1,b_1,...),(a_2,b_2,...),(a_3,b_3,...),...)$, where a specific example might be: TestArray = ...
65 views

### Is it possible to lower the bitwidth of (floating point) numbers?

The answer to this question will most probably be a definite no. Nevertheless, I would like to know whether it is possible to represent reals in the memory on less than the standard 32 or 64 bits ...
72 views

### How to accelerate updating some parts of sparse matrices?

I am trying to update some parts of an specific matrix as rapidly as possible. In what follows, I first set up the basics things that I want to use ...
154 views

### Mathematica Complains about Non Symmetric Covariance matrix, when it's not the case

I was doing some fitting with Mathematica7 using NonlinearModelFit. It's quite long the program to do the fit and that's why I am not displaying here ... It goes ok, and I can get the fit parameters ...
386 views

### Can RowReduce work in this matrix?

The matrix $Q$ with dimensions $n\times2*n*m$ is structured by $$Q=[B|AB|\cdots|A^{2*n-1}B]$$ where $Q$ is an augmented matrix built from a $3\times3$ matrix, $A$, and a $3\times2$ matrix, $B$. I ...
577 views

### Orthonormalization of non-hermitian matrix eigenvectors

When using Orthogonalize[] one can specify which definition of "inner product" is to be used. For example, ...
145 views

### MatrixForm explanation as why row extract is displayed as a column?

I have a 5 x 5 matrix: cdsSpread5yrs = But after doing a row extract, why is it displaying as a column? ...
408 views

### Finding eigenvalues of a $1500\times1500$ matrix

I need to find the eigenvalues of a $1500\times1500$ real symmetric matrix given by $A_{i,i+1}= A_{i+1,i}=-1$ and also $A_{1,N=1500}=-1$ (this is because of a periodic boundary condition used) and all ...
141 views

Here is the Problem how to find out the Saddle Point inside Matrix. m = {{9, 3, 1, 8, 0}, {6, 5, 4, 6, 7}, {2, 4, 4, 3, 8}, {5, 6, 2, 2, 1}}
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### How can I shift the frame ticks to the corner of each element-cell in a Matrixplot?

I am using the following code,to create a Legend for my plot. I would like to shift (or re-position) the frameticks to the corner of each of the cell-elements instead of being in their middle. I ...
122 views

### How to modify a matrix to satisfy a special condition?

I have matrix like this: How do I modify this matrix to make it satisfy the following condition: For each element {i, j} in the matrix the sum of the elements of row i must be equal to the sum ...
120 views

### Test First row of matrix

What is a good way to test the first row of a Matrix to check if one of the values equal a value. For instance, In this example, I want to get vector in the second row that has the bigger value in the ...
573 views

### Passing a matrix as a function argument

I am trying to do the following: ...
156 views

### A matrix-vector cross product

I want to do a cross product involving a vector of Pauli matrices $\vec \sigma = \left( {{\sigma _1},{\sigma _2},{\sigma _3}} \right)$; for example, $\vec \sigma \times \left( {1,2,3} \right)$. ...
271 views

### Is there a way to do conditional matrix loop using 'continue'

I have the following: ...
141 views

### Solving an equation involving a determinant

I have a matrix which doesn't include numerical values. There are four variables in it. It is defined by ...
199 views

### Find an inverse matrix, regarding a parameter as real

I have the matrix ...
127 views

### Numerical comparisons of matrices

I have a matrix which should be equal to a null matrix. However due to the numerical precision, a brutal equality test with a matrix initialized with zeros does not work. How should I perform the ...
79 views

### How do I plot Numerical Range of two hermitian matrices

Let $A_1$ and $A_2$ be two $3\times 3$ hermitian matrices. Then their numerical range is defined as two-dimensional set \begin{align} \mathbb{S}=\{\left[u^HA_1u,u^HA_2u\right]\in ...
91 views

### Optimizing functions taking matrix arguments

I'm looking for general information on how to optimize matrix valued functions, I have the following function I'm looking to maximize (or figure out if this is possible at all). ...
117 views

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### Mass Symbolic Manipulation with Subscripts? (from plaintext Input)

The simplest example of the change being sought is a greek letter, typed in as plaintext nu, and its may be replaced by the symbol, Î½: expr = 3nu*kx*ky+ ...
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### Optimizing a simple calculus using a list of matrices - Repeated dot product between a vector and a list of matrices [closed]

I want to make the following operation :  \begin{bmatrix} \dot q_1\\\dot q_2 \end{bmatrix} + \begin{bmatrix} \begin{bmatrix} q_1 & q_2 \end{bmatrix} \mathbf A_1 \begin{bmatrix} q_1\\ q_2 ...
44 views

### How do I access the binary matrix underlying an EdgeDetect output?

Applying EdgeDetect to an image generates a black and white edge-detected image, which I suspect corresponds to an underlying binary matrix. How can I access this ...
38 views

### Replace a specified portion of an array with elements from another smaller array

This may be a trivial question, but I have been at it for a couple of hours and I have not made much progress. I have a 10 x 10 array (T) that I have used to generate an 8 x 8 array (Q). I want to ...
43 views

### Expanding Matrix Expressions

I want Mathematica to recognize that A.(-B.C)+A.B.C = 0 Yet FullSimplify and the like leaves the expression as it is. How do I get around this?
181 views

### Tridiagonal matrix for any n

I'm pretty new to Mathematica and I need to figure out how to create a $n\times n$ tridiagonal matrix for any $n$. I don't have the slightest clue where to begin. Edit: got this far, not sure how to ...
131 views

### Creating a matrix from the output of a variable inside a for loop

I would like to enter the results of the following loop inside a matrix as its elements: ...
535 views

### Matrix multiplication in Block Form symbolic calculation by Mathematica

I have a problem which requires taking product of two $10\times10$ matrices. I would like to do it by considering both matrices as $5\times5$ matrices such that each entry of both matrices is actually ...
158 views

### Different determinants on 2 different computers

Is there any way to force Det to do itself in a certain way? I've been running the same notebook on 2 differents computer, one MacOSX Lion and one W7 (both 32bit) ...
68 views

### changing a symbol into a function variable

Struggled for a while on this problem and hopefully you can help... I have a mathematical expression that currently has a symbol where I used to have a function variable. How do I make the symbol ...
296 views

### Total Variation Distance of probability matrix

How can I calculate the Total Variation Distance of a transition Matrix? is there any built in function? I've searched all documentation and haven;t found anything. ** More information: Let me try ...
56 views

### Fast calculation of commute distances on large graphs (i.e. fast computation of the pseudo-inverse of a large Laplacian / Kirchhoff matrix)

I have a large, locally connected and undirected graph $G$ with $\approx 10^4$ vertices and $\approx 10^5$ to $\approx 10^6$ edges. Moreover I can bound the maximum vertex degree as $Q_{max}$. I ...
130 views

### Can I reduce a matrix inequality such as $\mathbf x^\prime\mathbf A\mathbf x > \mathbf x^\prime\mathbf x$?

I'm new to Mathematica. When I do linear algebra, I wonder if I can have an inequality such as $\mathbf x^\prime\mathbf A\mathbf x > \mathbf x^\prime\mathbf x$, where $\mathbf x$ is a column vector ...
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### How do I combine the data from two tables according to a rule of my own devising?

I have two matrices a = m x 5 and b =m x 5 (m is large, say 1,000) which are already sorted as below: How to generate a new matrix c = m x 5 which consists: Column 1: exact replica of Column 1 ...
135 views

### extracting the rows of a matrix satisfying a condition (e.g. all elements negative)

I have a matrix with thousands of rows and want the submatrix comprising the rows of the original matrix that have, e.g. a negative element in column 3. How to do that?
99 views

### Computing distance matrix for a list

Using functional programming in Mathematica, how can I compute a distance matrix for every element in a list of matrices... The distance would be computed between the item in the list and a "target ...
145 views

### More than one expression in the Table[] command?

I would like to construct a Matrix using the Table[] command. The issue is that I would like to use more than one expression for it. What I need to obtain is something like this : ...
250 views

### Matrix Multiplication Modulo 2

I would like to perform matrix multiplication modulo 2. Hence, instead of the usual: A.B I did: ...
I have been trying to compute eigenvalues of a rather sizable matrix A, about $500 \times 500$ (but sparse). I asked Mathematica to compute ...