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.

Filter by
Sorted by
Tagged with
1
vote
1answer
64 views

How to find the p-norm that meets the requirements?

On page 183 of this book there is Theorem 3: In other words, if the spectral radius of a matrix B is less than 1, there must be a norm $ ||B||_{p}$, so that $||B||...
3
votes
5answers
216 views

Simplifying away imaginary part

I'm solving the following eigensystem, and I get result which looks complex-valued. I expect the result to have 0 imaginary part, can anyone see a way to simplify it away? ...
6
votes
0answers
154 views

SemidefiniteOptimization for operator norms: Stuck at the edge of dual feasibility

Can someone give a workaround and/or explanation why Problem 1/Problem 2 fail to solve through SemidefiniteOptimization? Problem 3 works. (I'm using 12.1.0 on Mac). ...
0
votes
2answers
84 views

Mathematica is saying both inequality are false [closed]

I'm trying to ask Mathematica to compare 2 different values in inequality but it keeps saying "False". I put the code I'm running below. Thanks in Advance for any hint on what is problematic ...
-1
votes
1answer
70 views

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?
4
votes
1answer
180 views

Plotting conformal mappings: $(x, y) \mapsto (x^2, y)$

I'm currently studying transformation geometry, and I've been trying to figure out a good way to plot conformal mappings on $\mathbb{R}^2$ of the form $$ \mathbf{f} : \pmatrix{x \\ y} \mapsto \pmatrix{...
0
votes
0answers
51 views

Eliminate doesn't work

I tried to define r by the polynomials a,b,c only. The result which I want is r=4/3 a. But this eliminate doesn't work! It is continue running without stop and without any output. Eliminate[{a == x[1] ...
0
votes
2answers
87 views

Problem for defining continuously 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: ...
1
vote
1answer
82 views

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....
1
vote
0answers
92 views

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: ...
0
votes
0answers
60 views

Seeming inconsistencies with "Eigenfunction" [duplicate]

I am working on a problem which involves calculating the spectrum of a family of 2970x2970 Hermitian matrices. I have done similar things with Mathematica in the past, but this time there is an odd, ...
0
votes
0answers
26 views

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 <...
0
votes
1answer
71 views

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, ...
-2
votes
1answer
63 views

what is the difference between two Eigenvalue[...] outputs

Can someone explain the difference between two types of Eigenvalue[...] operations: ...
3
votes
1answer
81 views

How should I define the Cayley transform?

I am a beginner to Mathematica. I am trying to define a function which would evalute the Cayley matrix transform, namely taking a matrix $M$ such that $I + M$ is invertible to $(I-M)(I+M)^{-1}$. I ...
2
votes
1answer
92 views

How to solve this kind of matrix equation related to rank

I saw a post here to solve the rank relation equation of matrix: ...
5
votes
0answers
69 views

Effectivelly using Compile for calculate a Unitary transformation

I am new to Mathematica, and this is my first post, so if my question is not clear enough, I would be glad to read the comments and edit my question to add more information. The problem I need to ...
0
votes
1answer
148 views

How to transform a matrix into a diagonal matrix by Schmidt orthogonalization

I want to diagonalize a matrix by orthogonalization, but the following method cannot get the correct result: ...
0
votes
0answers
67 views

Matrix calculation and calculus in general form

Can Mathematica do the followings? (Note that dimension of matrices are given by general parameters like $m,n$) Can it do matrix calculation in general form? For example solving the following ...
2
votes
1answer
112 views

Non-valid modulus when using LinearSolve

I have a system of linear equations I want to solve mod 4, and I happen to know the solution, but I get an error when trying to solve it using LinearSolve. I define the matrix ...
0
votes
1answer
140 views

How to find a solution of this matrix equation quickly

I need to solve the following matrix equation to find a set of solutions for matrices A and Q which satisfy the conditions. <...
0
votes
2answers
121 views

How to quickly find a set of solutions that meet the requirements

Note: The following questions are from the 21th question of the 2010 Chinese Graduate Mathematical Entrance Examination (first set): It is known that the canonical form of the quadratic form $f\left(...
0
votes
1answer
80 views

Diagonalize matrix but keep the order of basis

I have a unitary matrix $U$ UMatrix. It looks like ...
0
votes
0answers
68 views

Is possible to make RowReduce more efficient?

I have huge matrices (not square ones, the rows are many more than columns), like 85k rows and 50k columns. I would like to use RowReduce on these, but it takes too much time to do that. I need to ...
1
vote
0answers
158 views

Removing Unwanted Eigenvalues, Twisted bilayer Graphene Hofstadter Butterfly

I am plotting eigen values of a matrix. I want to remove unwanted eigenvalues from the plot. For try run this is possible to manually remove these unwanted eigen values. But for actual run this is not ...
0
votes
0answers
61 views

Mathematica precision on extensive eigenvalues calculations

Im trying to evaluate some dot products with eigenvectors and matrices using Mathematica. My problem is the following: To an given matrix 6x6: ...
-1
votes
1answer
379 views

How to write a more concise `RowReduce` function that can deal with symbolic matrix?

I asked a similar question in this post before and understand the reason why RowReduce function can't reduce symbolic matrix. I wrote an ...
2
votes
1answer
149 views

Why sometimes eigenvectors matrix cannot transform to initial matrix?

As we know, $$H=U^{-1}\Lambda U $$ where $\Lambda $ is the diagonal matrix and $H$ is the original matrix, $U$ is the eigenvector matrix. Also, we can restore the original matrix via: $$\Lambda=UHU^{-...
0
votes
0answers
73 views

How to join the lhs and rhs of the rows of a matrix equation and solve for one of the variables?

The matrix equation m.{x,y}==b results in an awkward disjointed looking presentation but correct construction of a system of linear equations ...
1
vote
0answers
68 views

How to define an `MatrixReduce` function that can reduce the symbol matrix to the simplest type

The RowReduce function of MMA can not effectively reduce the matrix with parameters to the row simplest type. ...
0
votes
2answers
165 views

How to solve for y for a set of implicit (in x and y) linear equations for use in Plot?

From a matrix m={{1, 1}, {-1, 1}}, a vector b={1, 2}, and a list of variables vars={x,y} we ...
2
votes
1answer
250 views

How to solve this equation with rank relation of matrix

It has been known that matrix A is equivalent to matrix B, and I want to find the possible value of parameter ...
0
votes
0answers
80 views

How to deal with this problem of abstract matrix

First question: Let A and B be n-order square matrices, and r(X) denote the rank of matrix <...
0
votes
1answer
98 views

How to solve this equation with matrix rank condition

It is known that quadratic form $f\left(x_{1}, x_{2}\right)=x_{1}^{2}-4 x_{1} x_{2}+4 x_{2}^{2}$ can be transformed into quadratic form $g\left(y_{1}, y_{2}\right)=a y_{1}^{2}+4 x_{1} x_{2}+6 y_{2}^{2}...
1
vote
2answers
87 views

How to change the expression of the result of function `LinearSolve`

I want to solve the following linear equations: $$\left\{\begin{aligned} x_{1}+3 x_{2}+x_{3} &=0 \\ 2 x_{1}+6 x_{2}+3 x_{3}-2 x_{4} &=0 \\ -2 x_{1}-6 x_{2}-4 x_{4} &=0 \end{aligned}\right.$...
5
votes
2answers
534 views

Finding the similarity transformation between two matrices

I have difficulty in finding the transformation matrix of two similar matrices. It is known that matrix $A=\left(\begin{array}{ccc} -2 & -2 & 1 \\ 2 & x & -2 \\ 0 & 0 & -2 \end{...
6
votes
3answers
553 views

Multivariate linear regression

Say I have a 4-dimensional data set with two independent variables x1, x2, and two dependent variables y1, y2, i.e. each row is <...
2
votes
1answer
127 views

Numerical integration of MeijerG function with variables

I applied the integration, How to solve the function which is mentioned below. here, 'theta' is the only variable. q13, q1,q2,p,qi1 are all variables will take value from the loop ranges from 0 to 2, ...
0
votes
1answer
134 views

How o use singular value decomposition function to find the natural frequency and mode shapes

I have a matrix R which is having a dependency on ω, I am interested in finding the natural frequency and mode shapes of this matrix using SVD how to do this?. The regular way is to take the ...
3
votes
2answers
133 views

What am I doing wrong using FindIntegerNullVector?

Most of the time when I use FindIntegerNullVector with inexact numbers, I get useful results. But occasionally, it seems to miss finding a simple null vector. Example: ...
1
vote
1answer
99 views

Making function from data by using interpolation

I Have two set of data separately, which one of them is pressure and the other one is energy density.(P: pressure, E: energy density) I want to use these data as a function, P(E) or E(P) by using ...
6
votes
1answer
207 views

Derivative of real antisymmetric matrix in mathematica

Is it possible to find the derivative of components of a real antisymmetric matrix using index notation? Eg: I have a very large real antisymmetric matrix. Then from Matrix Cookbook, we know the ...
2
votes
1answer
76 views

Find non-unique Hermitian solution to pair of matrix equations

This is a continuation of my previous question here, but I previously did not fully specify some of the restrictions on the matrices and so the solutions posted there were not that helpful. I'm ...
3
votes
0answers
72 views

Prime Matrix with determinant of powers $2^x$

Mathematica has commands for finding prime matrices, for example, here is a matrix with randoms in the range $<100$: RandomPrime[100, {3, 3}] This $2 \times 2$ ...
3
votes
1answer
144 views

Solving Inequalities using Mathematica

How can I solve this inequality using Mathematica? Sqrt[B^2 + J^2] Cosh[(2 J)/T ] < J Sinh[ (2 Sqrt[B^2 + J^2])/T] where T, J, and B are reals and they are >...
0
votes
1answer
31 views

Difficulty refactoring a graphics point from displaying a tooltip to a label when using show to combine point with a plot

I have a Plot[...] of a system of linear equations and a function graphicsPoint[...] that generates a graphics point to show ...
2
votes
1answer
139 views

Solving symbolic system of non-linear equations takes too long

I am trying to solve a set of system of symbolic non-linear equations: ...
1
vote
1answer
81 views

Solve won't find solution to simultaneous matrix equations

I'm trying to solve a pair of simultaneous matrix equations of the form, $$AX + XA^\dagger + BJB^\dagger = 0,\ \ X C^\dagger + B J D^\dagger = 0,$$ where, $$J = \begin{bmatrix}1&0\\0&-1\end{...
2
votes
1answer
116 views

LeastSquares vs ArgMin

From the documentation, we learn that: LeastSquares[m,b], when b is a vector, is equivalent to ...
1
vote
1answer
454 views

How to obtain non-trivial solution?

I have the following system of equations. $ quad\quad\quad\quad u+\alpha v+v+e^{\frac{i \alpha }{2}} (\alpha -1) x=\alpha u+e^{-\frac{1}{2} (i \alpha )} (\alpha +1) z, +u+v=\alpha (v+w)+w+y, (\...

1
3 4
5
6 7
28