# Tagged Questions

0answers
75 views

### Symbolic matrix calculus: What's new in Version 9

I have seen some of the related posts, which ask about doing matrix calculation on tensors unknown dimensions. One of the posts mentioned that version 9 has some capability, but it was concerned about ...
1answer
80 views

### Calculate the algebraic multiplicity of known eigenvalues of a large, sparse matrix

I have a large (and sparse) matrix with size 1000x1000 -- 10000x10000. I believe i know all eigenvalues for the matrices. All entries are integers and so are the eigenvalues. I want to check this by ...
0answers
46 views

### Find the values of parameters so that the matrix is symmetric positive definite

Good evening , I have a matrix 20x20 in symbolic form. The matrix depends on 5 parameters (a,b,c,d,e). I would like to get the interval of each parameters that ensures that the matrix S is symmetric ...
0answers
62 views

### Computing residues of matrix valued functions symbolically

I have a somewhat specific application in mind, but I've run into this kind of problem a few times and never found an elegant solution. Is there an efficient way to get Mathematica to recognize that ...
1answer
194 views

### Symbolic scalar-by-matrix derivative

Let's say I want to calculate the following scalar-by-matrix derivative $$\frac{\partial}{\partial A} \text{tr} \left[(\vec X^T A)^T (\vec X^T A)\right],$$ with $\vec X$ and $A$ being a $n \times 1$ ...
0answers
106 views

### Eigenvectors for a large symbolic matrix

I'm trying to compute the eigenvectors for a 42x42 symbolic matrix (with one variable) in Mathematica. I get the following error: Eigenvectors::eivec0: Unable to find all eigenvectors. >> and the ...
1answer
442 views

### How to find the inverse a symbolic matrix that Mathematica thinks might be singular

I have a square matrix depending on a parameter "a". When "a" has a numeric value (eg 2.1 * 10 ^ 8) through the inverse function Inverse[] I can invert the matrix. If I write the matrix as a function ...
0answers
141 views

### Speeding up inversion of symbolic matrices by invoking caching

Is it possible to reduce the computation time taken to find inverse of symbolic matrices USING CACHING TECHNIQUES accessible (if any)? I am trying to compute inverse of symbolic matrices of size ...
0answers
55 views

### eigenvalues and eigenvectors without Root answers

I'd like to find eigen values and vectors of parametric 21*21 Matrix and i cant solve the root problem.please help me to find the answers without Root. My Matrix is: ...
2answers
132 views

### setting real parameters in Hamiltonian matrix

The following Matrix represents my Hamiltonian. m = {{ B/2 - d - j/2 + a, (Sqrt[2]*j)/2, M}, {(Sqrt[2]*j)/2, B/2 + a, 0}, {M, 0, (-3*B)/2 - d + j/2 + a} How can ...
2answers
120 views

### How to display output as symbols?

I have this piece of code which populates a matrix following different rules depending on row and column number: ...
1answer
182 views

### Symbolic matrix simplification and solving

I am trying to expand or solve an equation that contains matrices for a certain matrix, but it is not working: ...
0answers
191 views

### Solving for equilibrium distribution (symbolic) by matrix multiplication

I have a huge transition matrix (81x81). The matrix is too huge to paste here, so I store it in this notebook. (There are constraints on the symbols: $0<p_b<1$ and $0<p_g<1$. If further ...
2answers
186 views

### Mixed product identity between tensors in Mathematica 9

How can we simplify tensor expressions in Mathematica 9 using the mixed-product identity $(A\otimes B)(C \otimes D) \equiv AC \otimes BD$ ? Is it possible to implement this kind of evaluations using ...
1answer
585 views

### How to simplify symbolic matrix multiplication results?

I've defined three symbolic abstract matrices X, M and S as shown below. ...
1answer
298 views

### How can I get Mathematica to recognize equality of symbolic matrix expressions?

I have two matrix expressions: X.Transpose[T].Transpose[X] and X.T.Transpose[X] I want Mathematica to recognize that ...
1answer
116 views

### Trouble carrying out symbolic operations on matrixes

I have some problems. First of all, I declare matrices like below ...
3answers
343 views

### RowReduce for symbolic matrices

I'd like to invoke RowReduce on some matrices with a time parameter. For example consider A = {{1, 0}, {0, t}} If ...
0answers
459 views

### Analytically solve the eigenvalue problem with infinite dimensions by Mathematica?

If I am given a symbolic expression of all the matrix elements in an infinite-dimensional space, e.g., the Hamiltonian of a quantum mechanical system, is it possible to get the symbolic expression for ...
1answer
146 views

### Pattern match with Table for matrix dimension check

In Mathematica, often an expression involving matrices will encounter dimension mismatch errors, like we are multiplying a 3x2 matrix to a 3x4 matrix. Below we define a new symbol Dim, which can be ...
2answers
359 views

### 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, ν: expr = 3nu*kx*ky+ ...
0answers
35 views

### Symbolic Calculations with formal matrices [duplicate]

I want to make calculations with matrices in the form (for lovers of statistical mechanics, is just the first step replica symmetry breaking) ...
1answer
196 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 ...
1answer
399 views

### How to efficiently fill in matrix values?

I would like to efficiently fill in or assign values to matrix m: m={ {a[1,1],a[1,2],a[1,3],a[1,4]}, {a[2,1],a[2,2],a[2,3],a[2,4]}, {a[3,1],a[3,2],a[3,3],a[3,4]}, ...
1answer
264 views

### Verifying and deriving basic (block) matrix identities

How can I use the new symbolic matrix/tensor capabilities to verify matrix identities, such as (1) or (2) Even better, how can I ask Mathematica to derive expressions for X, Y, Z, and U like ...
2answers
226 views

### Symbolically associate vectors and their norms

I am wondering how to handle the following situation: I do have vectors of known dimension that I would like to handle symbolically. I suppose I can do something like ...
2answers
895 views

### Non-commutative symbolic linear algebra

I am fairly new to Mathematica but I thought I would be a helpful tool to carry out a few simple linear algebra calculations. It seems like an easy task but I cannot figure out how to do it. For ...
3answers
2k views

### How to symbolically do matrix “Block Inversion”?

Consider a block (partitioned) matrix matrix = ArrayFlatten[{{a, b}, {c, d}}] where, a, ...