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.
1,566
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Mathematica's definition of cos(kA) where A is the 1st Pauli spin matrix
For a homework assignment I was asked to derive the formula of $e^{ik\sigma_{1}}$ - where $\sigma_{1}$ is the Pauli spin matrix {{0,1},{1,0}} - using the Taylor ...
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0
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65
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Solving a linear algebra problem containing minimal polynomial degree
Consider a set of three-dimensional points ${\left\{{\left(a,ab,abc\right)}~\middle\vert~a,b,c\in\mathbb{N_+}\land a+b+c\leqslant2023\right\}}$. If there exists a non-zero real polynomial $\...
- 385
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How to create an n-by-1 matrix from user-input values? [closed]
I want to create a n-by-1 matrix for any n inputed by the user. Also the elements in the matrix should be entered by the user.
1
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2
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Can you recover the original vectors that, when summed together, achieved a particular criteria
I am wondering if it is possible to take the binary strings of length $3$ (tuples) whose sums have weight $2$ (i.e they have $2$ non-zero entries)(binary case, meaning they have two $1$'s entries) $$u ...
- 417
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1
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How to find and delete the duplicates from lists of vectors
What I want to do is to take a list of vectors:
u={{1,0,0,0},{0,1,0,0},{0,0,1,0}}
v={{1,1,1,1},{1,0,0,0},{0,1,0,0}}
I want to find the duplicates between u and v ...
- 417
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0
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65
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Mapping two pure functions over different lists
Say if I have two lists of vectors of the same length, for example:
u = {{1,0,0},{0,1,0},{0,0,1}}
v = {{1,0,1},{1,1,0},{1,1,1}}
I want to add (modulo 2) ...
- 417
1
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2
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How to delete duplicate lists of vectors (in any order) from a list of lists?
I have a list of vectors:
v={{{0,0,0},{0,0,1},{1,1,0}},
{{1,0,0},{1,1,1},{0,1,1}},
{{0,0,1},{0,0,0},{1,1,0}}}
Clearly, the first entry and the third entry contain the same vectors. I want to delete ...
- 417
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1
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58
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Commutant of set of matrices
I'm trying to compute the commutant of a set of matrices, so the set of matrices that commutes with all matrices in the original set.
I'm a complete newbie with mathematica, so I would be greatful for ...
- 43
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1
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63
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Gauss elimination with pivoting error
I am attempting to write code for Gaussian elimination with pivoting. I need my code to be able to find the maximum pivot in the column and swap the rows to ensure that the first element is always the ...
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1
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218
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Nullspace if denominator is zero
This question is based on a previous question where the matrix
mat = {{0, s, 1, 0}, {-s, 0, 0, 1}, {1, 0, 0, -s}, {0, 1, s, 0}};
is given and one wants to determine ...
- 654
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1
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Transition to a new basis with rotation of one of the axes [closed]
The lengths of the basis vectors e1 and e2 of the general Cartesian coordinate system on the plane are equal to 4 and 2, respectively, and the angle between the basis vectors is 120°. Relative to this ...
- 101
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1
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40
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How to define linear mappings on a vector space spanned by abstract symbols?
Say I have an infinite dimensional vector space $V$ with basis consists of abstract symbols $\{ a_j \}^\infty_{j=0}$, and consider a linear function $f$ on $V$ defined by its action on the basis ...
- 119
1
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1
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Simplify to vectors and matrices [closed]
How do you simplify an expression:
$[r_1, r_2, r_3]^T [t_1, t_2, t_3] = r_1 t_1 + r_2 t_2 + r_3 t_3 = \vec{r}^T \vec{t}$
In other words, I want to group and simplify scalar expressions over vectors / ...
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1
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How to explore the unchanged eigenvalue with the largest real part?
The provided code below employs the Chebyshev collocation method to calculate eigenvalues. I'm interested in examining the eigenvalue with the largest real part while ensuring it remains almost same ...
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2
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2
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59
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Generalized scalar product for matrices
Let $X$ and $Y$ be matrices of a dimension $ m \times n $. I would like to keep $m$ and $n$ as a variable and define a scalar function $$ \operatorname{scalar}: X , Y \to \mathbb R$$
$$
\...
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1
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Solving the system of equation with the expression of total differentiation using Cramer's rule
I want to solve the following system of equations of total differentiation using Cramer's rule.
And I got the following message:
where d is delta as the symbol of ...
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2
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100
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How to find codewords from constraint equations? [closed]
I have edited this question to include more information about what algorithm I wish to use etc.
Say if I have a linear binary code with parity check matrix
$$H = \begin{bmatrix}
0 & 1 & 1 &...
- 417
1
vote
1
answer
126
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What is mathematica command for finding eigenvalues of a generalized eigenvalue problem?
The provided code below is designed to compute the eigenvalues for the problem I inquired about earlier in this post: How to find eigenvalues?. I believe my code is mostly accurate, with the exception ...
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Eigenvalues and classification of critical points [closed]
I started with a function (x,y) and tried to write the code to work out the eigenvalues and classify the critical points.
The output it all good up until I try to use Which[] to classify the critical ...
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How to find linearly independent linear combinations of a set of vectors (general case)
If I have a list of vectors, say $v=\{v_{1}, v_{2}, \dots ,v_{n}\}$.
Is there a way that I can get all linearly independent linear combinations of these vectors, such that if I change the content of ...
- 417
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1
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how to solve problem involving a condition?
I am new to mathematica, therefore this might be a pretty simple question,
My problem is for example: Compute the eigenvalue for matrix A= {{1,c},{1/c,1}}, c>0.
when the matrix becomes more ...
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How can I prevent conversion of a SparseArray to a DenseArray?
The Problem
I'm trying to implement an efficient Whitker-Eliers smoother in Mathematica. In Matlab, this is a few lines of code (taken from the SI of the above paper):
...
- 490
1
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2
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Radially symmetric SmoothHistogram3D?
I have a sample from a distribution invariant w.r.t rotations around 0. What's the best way to incorporate this information into a smooth 3D histogram?
...
- 8,059
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Eliminate a variable from two equations with trigonometric functions
I am trying to eliminate theta from the following two equations but in vain. I tried the command Eliminate and Reduce.
...
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95
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Mathematica fails to correctly recognize Hermitian matrix
I have a Hermitian matrix, but Mathematica gives 'False' when I try with HermitianMatrixQ.
...
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56
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1
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0
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78
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Getting behavior around 0 for spectrum of product of Gaussian matrices?
Edit the math part was answered in mathoverflow, I'm now looking on how to port this to Mathematica to check against observed fit
Consider a product of $k$ independent square matrices with IID ...
- 8,059
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75
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Why does `LinearSolve` give this solution for a singular matrix?
I want to solve the matrix system Ax+b==0, the equation is as follows (In MATHEMATICA code, I use AA and ...
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Does the solution exist in this matrix system?
I got these equations after the post process, so I just listed the numerical equations, and there are 50 equations total with 50 unknown variables, however, the
...
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Solution to a vector recurrence equation
Suppose $n\ge1$ is fixed. Let $C_1,C_2,\ldots,C_n$ be given constants.
Consider the recurrence
$$
C_n[S_{1}^{(n)},S_{2}^{(n)},\ldots,S_{n-1}^{(n)}]=
\left[\binom{n}{1},\binom{n}{2},\ldots,\binom{n}{n-...
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Comparing two power series and extracting their coefficients
I have a standard mathematical problem that I was wondering how to solve efficiently by mathematica. Here is the problem.
I have two power series expansions of a function ...
- 417
3
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1
answer
270
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SVD decomposition with optimization
Let's suppose there is a matrix A nxn, which will be decomposed into SVD:
where ui and vi are singular vectors composing matrix U and V. sigma is a vector that contains the eigenvalues. In ...
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2
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Reshaping sparse arrays to have extra index
I have an $n \times m \times p$ array, let's call it $r$.
I want to obtain an $n \times m \times p \times 5$ array (let's call it $q$) where $q$ is the same as $r$ except that every non-zero component ...
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Solving system of linear equations in specific order
I know how to solve set of linear equations using Solve, or by hand of course. However, my current problem requires me to solve the equations in a specific order, ...
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Eigenvalue function finds real eigenvalues for antihermitian matrix
If given a (large) antihermitian matrix, Mathematica occasionally finds real eigenvalues although the in-build function AntihermitianMatrixQ confirms it to be antihermitian. The matrices for which I ...
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1
answer
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MatrixExp[] for 4 by 4 matrix gives an unavailable answer [duplicate]
Q = ( {
{-7, 1, 2, 4},
{2, -4, 1, 1},
{2, 2, -6, 2},
{1, 1, 1, -3}
} )
MatrixExp[Q*t]
I defined the matrix Q and executed the command. Then I ...
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2
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53
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Transformation invariant subspace of three-component array
I have a large sparse array A with dimensions $m \times n \times q $. I also have two transformation matrices, B ($n \times n$) ...
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0
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How to judge whether this equation group really has no solution?
I have got the following equation using the following code after the preprocess. The preprocess is complicated so cannot be displayed here in limited scale, and assuming that the following equations ...
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0
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Calculate the integral of the Slater determinant
This is a Slater determinant:
$$
s=\left|\begin{array}{ll}
\psi_{1 s}\left(r_1\right) \alpha & \psi_{1 s}\left(r_1\right) \beta \\
\psi_{1 s}\left(r_2\right) \alpha & \psi_{1 s}\left(r_2\right)...
- 1,382
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86
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How to get Mathematica to carry out my computation of a vector norm fully?
I am relatively new to Mathematica, and I have come across the problem where Mathematica often doesn't seem to carry out calculations fully. For example: I have a vector v and want to find its norm, ...
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How to obtain the linear equation passing through two coordinates？
{-Sqrt[5], 0}, {3/Sqrt[5], 4/Sqrt[5]}
How to automatically obtain the straight line equation passing through two points with the coordinates of the two points as ...
- 2,705
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Gaussian Matrix Model - Large N Expansion Physics with Mathematica
Update: Attempted 2nd time by replica method
I'm trying to implement basic large N expansion in Mathematica.
I'm trying to understand what this means on the fly as well.
The model I am trying to ...
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2
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292
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Show steps in finding the reduced row echelon form of a symbolic matrix
I would like to figure out a way to see the row operations RowReduce uses to arrive at the reduced row echelon form of a symbolic square matrix.
Solutions that show ...
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2
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Find an orthonormal basis for column space without Orthogonalize [duplicate]
How can I find an orthonormal basis for column space of the following matrix without using Orthogonalize?
$$ \begin{bmatrix}
-10 & 13 & 7 & -11 \\
2 &...
2
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0
answers
58
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Computing residue of the resolvent
I'm looking at this Mathematica tutorial
where the author defines matrix function by summing over (matrix-valued) residues of the resolvent.
...
- 8,059
8
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1
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115
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Rank of singular, large, sparse matrices
I need to find the rank (and eventually do the Gaussian elimination) of a large, sparse, non-square matrix of integers. There are a few methods in Mathematica to find the rank of a non-square matrix (...
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How can I construct a determinant-type differential operator?
How can I construct a determinant-type differential operator, where the multiplication of elements in the determinant represents the composition of multiple differential operators?
\begin{align*}
\...
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