# 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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### Inverse of a matrix with symbolic variables

I want to evaluate the inverse of the following colossal matrix ...
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### Solving complicated linear system [closed]

I have this system and I would solve it with mathematica, I try with the instruction Solve but I have an error Please help me.
1 vote
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### Solve the current equation with respect to one of the coefficients and substitute it into each equation of the system

Good day to all! In this question about recurrence relations, I had a simple case when the k + 1th variable is represented in terms of ...
62 views

### Solve coupled differential equation using Matrix

I am a complete beginner to Mathematica. I am trying to solve the following equation: $\frac{d}{dt}\rho_t = -0.5* \eta* \Gamma[\rho_t]$, where $\Gamma[\rho_t]$ is a 4x4 matrix whose coefficients are ...
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### Replace previous equations into the current one in a recurrence relation

I have a recurrence relation given as follows: f[k + 1] == 1/a[k, k + 1] Sum[a[k, k - k1] f[k - k1], {k1,0,k-1}] Evaluating it for ...
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### Change of basis matrix between symmetric matrices

I have two 5x5 matrices: ...
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### How to get exact solution for determinant in mathematica? [closed]

I am currently trying to program in mathematica, my issue is that the program is not solving for the exact value of the determinant in comparison to matlab. Code given below, where a and x are ...
60 views

### How to find non-trivial solution to homogeneous linear equations by Mathematica using code (Input form)?

I have many homogeneous equations to which I am interested to find the non-trivial solution using Mathematica, But I am totally new to Mathematica, so I do no know, how to find the non-trivial ...
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### Solve a homogeneous, linear system of algebraic equations with symbolic coefficients

Good day to all! I have a large system of homogeneous algebraic equations with symbolic coefficients. The following simplistic piece ...
1 vote
106 views

### How is MatrixPower computed?

How does Mathematica compute MatrixPower[m,n]? The documentation states it is equivalent to Dot @@ ConstantArray[m, {n}], but ...
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1 vote
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### Solving a linear algebra problem of the form "For what $x$ below vectors are linearly independent?"

Let $v_1,v_2, v_3, v_4$ be four vectors, parametrized by $e$. How can I solve the following type of the problem in Mathematica? For what values of $e$ four vectors $v_i$ are linearly independent? ...
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### showing that CylindricalDecomposition returns partition the space

I have 24 objects returned from eight calls to CylindricalDecomposition, say $exp_1$ ... $exp_24$. The objects are in the three dimensional reals, $(a, b, c)$, so ...
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1 vote
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### Mathematica introduces unneccessary/wrong square root of complex number

I'm trying to use Mathematica to get the eigenvalues of the following matrix: \begin{bmatrix} \epsilon & v + ue^{ika} \\ v + u e^{-ika} & \epsilon \end{bmatrix} Executing the following ...
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### Threshold on triangular SparseArray

I am confused by the behavior of Threshold on sparse UpperTringularize (and LowerTringularize...
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### Solve Riccati Equations by hand

I'm in the midst writing a bit about LQR problems and would like to show that some things in mathematica can be tested by trying to write such problems out by ones self, However I cannot seem to find ...
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1 vote
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### I am searching for the Eigen stuff of a non linear transformation

I have a slightly odd problem I have been working on as part of a project on probability models. The full problem itself is not relevant but here is where I am stuck. I have a 6D space $P$, where all ...
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### Transpose[m,{1,1}]

According to the documentation, Transpose with a second argument {1,1} on a square matrix returns the diagonal of the matrix. ...
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### Efficiently calculating half of the eigenvectors of a sparse array

Eigenvectors of a sparse array $\quad$ Problem statement I want to calculate the eigenvectors corresponding to the negative eigenvalues of an $8L^2 \times 8 L^2$ matrix ($L \sim 30 )$. Most of the ...
1 vote
39 views

### Eigenvalues broken for nonsymmetric matrices

It looks that eigensystem calculation can easily go broken with real nonsymmetric/general complex matrices. Here are two examples with the possibly complex spectra plotted in the complex plane. I'm ...
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### Normal equation of plane through a point and line

I need to find the normal vector of the form Ax+By+C=0 of the plane that includes the point (6.82,1,5.56) and the line (7.82,6.82,6.56) +t(6,12,-6), with A=1. Of course, this is easy to do by hand, ...
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