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.

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32 views

Problem in getting the full rank of a matrix

I have 17 equations I am trying to put them in the matrix form. I am trying to understand why the matrix is not full rank. ...
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Simple Question: Expand[(a + b)^2] in electrical communication research [closed]

Expand[(a + b)^2] I have two terms here, term a ...
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1answer
70 views

Simple Question: How to simplify what is inside the Sin function like below?

I have this code of Mathematica (1/(2 (fj - fk) π)) Cos[(fj - fk) π T + (fj - fk) π (T + δt)] Sin[(fj - fk) π T - (fj - fk) π (T + δt)] There are a few ...
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2answers
42 views

Solve the system using elimination What are a, b, and c in the quadratic equation, ax^2+bx+c=y given the [closed]

Solve the system using elimination What are a, b, and c in the quadratic equation, ax^2+bx+c=y given the points: (2,17), (-2,9), and (1,6), please solve the question using steps e.g. (step 1, step 2)?
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3answers
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Solving equation involving max-row-sum matrix norm?

I'm trying to solve for $\|A(a)\|_\infty=1$ where $A$ is a positive definite matrix parameterized by scalar $a$ and $\|.\|_\infty$ is max-row-sum norm of the matrix. For the problem below, I know the ...
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1answer
39 views

Solving System of Equations

I want to solve a huge system of equations which is generated using the Finite-Difference-Method. The Problem with that system is that it is badly conditioned and so ...
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3answers
48 views

Find The Value of a n-order Determinant

In Mathematica, we can find the value of a determinant with the built-in function Det. But how can I find the value of a determinant like this one? $$ \left|\begin{...
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1answer
55 views

Re-expressing equations [closed]

$$Y = \frac{1}{\sqrt{2}}D+\frac{1}{\sqrt{2}}U$$ $$X = \frac{1}{\sqrt{2}}D-\frac{1}{\sqrt{2}}U$$ I have above two equations. I want to rewrite the above equations in terms of D and U in Mathematica....
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53 views

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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1answer
44 views

How do you ask someone to input the values of a matrix?

I'm trying to set up code that basically asks the user to input the values of a matrix with a certain key size. I want them to first enter the keysize and then ask for all of the entries necessary to ...
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1answer
39 views

How to obtain eigenvectors in AceGen

I'm trying to obtain eigenvectors of a 3D plastic stretch tensor $C_p$. There is no SMSEigenvectors function, so I tried with ...
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48 views

linear interpolation error [closed]

I have two set of data for pressure and energy density and I used a linear interpolation to apply the data as a function in terms of each other. ...
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33 views

Getting non-trivial solution for a Homogeneous system of two equations which symbolically give trivial space

I have two supposedly homogeneous equations. Solve gives a trivial solution for them. Is there any way in Mathematica to extract non-trivial solutions for this ...
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2answers
101 views

How to define some functions automatically?

I want to use Gauss-Seidel iteration to solve this problem. $$\left\{\begin{array}{l} 8 x_{1}-3 x_{2}+2 x_{3}=20 \\ 4 x_{1}+11 x_{2}-x_{3}=33 \\ 6 x_{1}+3 x_{2}+12 x_{3}=36 \end{array}\right.$$ ...
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0answers
33 views

Reducing generalized eigenvalue problem to regular eigenvalue problem

I expected generalized eigenvalue problem on $(A, B)$ to reduce to eigenvalue problem on $B^{-1} A$ when $A$, $B$ are full rank (Section 7.1 of generalized eigenvalue tutorial), but I get different ...
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2answers
104 views

Logarithm of singular matrices

I wanted to calculate following quantity: $X=Tr[\rho_1 \log[\rho_2]]$, as in the relative entropy. Here, $\rho_1, \rho_2$ are positive semidefinite matrices with non-orthogonal support (so that the ...
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1answer
45 views

Degenerate matrix diagonalization

When you diagonalize a matrix, and two eigenvalues are degenerate, is there a way to ask Mathematica for specific eigenvectors? Thanks
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2answers
85 views

How to obtain the Gauss-Seidel iterative results in this form?

I need to use the Gauss Seidel iterative method to solve the linear equations $\left\{\begin{array}{l} 8 x_{1}-3 x_{2}+2 x_{3}=20 \\ 4 x_{1}+11 x_{2}-x_{3}=33 \\ 6 x_{1}+3 x_{2}+12 x_{3}=36 \end{array}...
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44 views

Solving multiple systems using Cholesky factorization to find Inverse of a matrix

I have a matrix: A = {{1, 1, 1, 1}, {1, 5, 5, 5}, {1, 5, 14, 14}, {1, 5, 14, 30}} I wrote code in Mathematica (mostly copying what professor gave us, I'm new to ...
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2answers
212 views

How to realize the inner product of function concisely?

A family of functions is known as $\left(\varphi_{0}, \varphi_{1}, \cdots, \varphi_{n}\right)$. I'd like to know how to express their inner product conveniently as follows: $$\left(\begin{array}{cccc} ...
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5answers
196 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? ...
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119 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). ...
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2answers
81 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 ...
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1answer
38 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?
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1answer
82 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{...
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47 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] ...
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2answers
39 views

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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0answers
83 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: ...
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0answers
59 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, ...
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22 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 <...
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1answer
64 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, ...
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1answer
40 views

what is the difference between two Eigenvalue[…] outputs

Can someone explain the difference between two types of Eigenvalue[...] operations: ...
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1answer
67 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 ...
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1answer
83 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: ...
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42 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 ...
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1answer
84 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: ...
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55 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 ...
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1answer
45 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 ...
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1answer
117 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. <...
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2answers
117 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(...
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1answer
54 views

Diagonalize matrix but keep the order of basis

I have a unitary matrix $U$ UMatrix. It looks like ...
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0answers
48 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 ...
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0answers
61 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 ...
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36 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: ...
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1answer
341 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 ...
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1answer
125 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^{-...
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39 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 ...
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0answers
61 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. ...
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2answers
76 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 ...
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1answer
188 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 ...

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