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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4
votes
1answer
177 views

Proving positive definiteness or semi-definiteness of a matrix

I have the following 4x4 real symmetric matrix: $K=\begin{bmatrix}3-3w & -\frac{4}{3}+a+2w & \frac{5}{12}+b-\frac{w}{2} & 0\\ -\frac{4}{3}+a+2w & -1-6a-3x & ...
2
votes
0answers
91 views

Simplify large fractions

Hi i'm quite new with Mathematica and i'm experiencing some problems with Simplify and FullSimplify. I'm dealing with a sistem ...
2
votes
1answer
224 views

Row echelon form question

I am wondering if there is a Mathematica command that will put a matrix in row echelon form. That is, put $$ \begin{bmatrix} 1 & 2 & 3\\ 2 & 3 & 4\\ -1 & 0 & 2 \end{bmatrix} ...
0
votes
0answers
45 views

How to tweak a symbolic RowReduce?

B = {{-1, 1, 0, a}, {-1, 1, 0, a}, {-1, 1, 0, b}}; MatrixForm[B] RowReduce[B] // MatrixForm Mathematica is indeed giving ...
2
votes
0answers
29 views

What is the most efficient method to find a single eigenvector with eigenvalue that is numerically 0?

I need to find an eigenvector of a (numerically calculated) square matrix M corresponding to the eigenvalue 0. The methods I know are ...
0
votes
1answer
103 views

Creating a random make matrix with a particular rank

Does Mathematica have a built-in function that will return a random mxn matrix with rank r?l
2
votes
1answer
100 views

Inverting matrix with assumptions

I want to invert a matrix that contains some variables, so I thought I should give some assumptions to Mathematica to speed up the process. How do I assume that $s0,...,s8$ are positive constants ...
2
votes
1answer
237 views

Why can't Mathematica compute the null space of these matrices?

I'm writing a library of functions to work with musical pitch-class vectors. One of my functions gives me a skew-symmetric matrix modulo 12 that corresponds to the differences between components of ...
0
votes
3answers
221 views

Calculating eigenvalues of a large matrix takes a long time

I have a tridiagonal matrix (1000×1000) with each element equal to $1$ except {n, n} = 2. It takes 8 hours to give me the eigenvalues?!! Here is the code I used: ...
0
votes
0answers
25 views

How to obtain the eigenvector corresponding to the minimal eigenvalue of a generailzed eigenvalue problem [duplicate]

Suppose I have the following input a = Import["d:\am.txt", "Table"]; b = Import["d:\bm.txt", "Table"]; c = Eigenvalues[N[{a, b}, 5]]; Min[c] where am.txt is 3.0 2.0 2.0 3.0 bm.txt is ...
0
votes
2answers
88 views

Zero division in linear equation solution

I'm trying to transform a vector to another coordinate system with different root vectors. The other root vectors are defined by three points in space that form a plane, and it's a normal vector. ...
-1
votes
1answer
63 views

Graphing a vector [duplicate]

I have a vector (in physic) designated asF1=250cos(60)i+250cos(60)j+250cos(45)k, and i would like to see it in a 3D graphic with the axis centered at the origin, after what i would include other ...
0
votes
1answer
185 views

How to plot and visualize a single linear vector in 3D? [closed]

I have a vector (in physic) designated as F1=250cos(60)i+250cos(60)j+250cos(45)k, and i would like to see it in a 3D graphic with the axis centered at the origin, after what i would include other ...
2
votes
1answer
272 views

Why do the eigenvectors for two similar matrixes differ by a large amount

I have two matrixes with values differs only slightly ...
0
votes
1answer
98 views

How to obtain a convergent solution iteratively for a linear system of equations

I am working on a problem that requires an iterative procedure to solve a linear system of equations, the system of equations in matrix form is: $$\underbrace{\begin{bmatrix} r_{11} & r_{12} ...
0
votes
1answer
78 views

Reduce Vector/Matrix mod N [closed]

If I have a vector such as below and want to reduce it mod a number, how can I do this? V = {{176}, {648}}; MatrixForm[V] MatrixForm[V, Modulus -> 26] Both ...
2
votes
1answer
124 views

Maximizing the number of zero entries in a matrix

I have a matrix with a bunch of parameters in its entries, they all come in different combinations in different places of the matrix. I can post the matrix itself if requested, but I think what I mean ...
1
vote
0answers
35 views

MatrixConditionNumber for 2-norm unexpected error [duplicate]

From documentation it has been specified that we can use 1,2 or as the second parameter of ...
9
votes
1answer
251 views

$3\times 3 = 6 + \bar{3}$ in Mathematica?

Can Mathematica handle this type of algebra, which is used very frequently in e.g. particle/nuclear physics? That is, I want to decompose a product of representations (in $SU(N)$ say) into irreducible ...
1
vote
0answers
190 views

Find the smallest eigenvalue (not absolute value ) for a generalized eigenvalue problem

Related post Find the eigenvector associated with the smallest eigenvalue, not smallest in magnitude I tried to find the smallest eigenvalue for a generalized eigenvalue problem A c= \lambda B c ...
3
votes
6answers
157 views

What is the range of values $x$ for which $f(x)$ is higher than $k$ over a given domain?

What is the easiest way to answer the following question in Mathematica: Given a function $f(x)=y$, what is the range of values $x$ for which $y$ is higher than some number $k$ over the domain of $x$ ...
1
vote
0answers
55 views

Confusing NullSpace Method behaviour

The background of this question is that I'm trying to get the bottom of when the output of NullSpace outputs a list of pairwise orthogonal vectors. On my route to ...
1
vote
1answer
106 views

Why `FindMaximum` doesn't work in my example

Consider the following function ...
1
vote
2answers
126 views

Is this caused by round-off errors?

Let's consider this integration Integrate[ E^(4 n x s) (1 - x)^(-1 + 4 n μ) x^(-1 + 4 n ν), {x, 0, 1}] It returns ...
-1
votes
2answers
194 views

How to compute LLL-reduce basis from lattice in Mathematica? And factor N

original article Clear. What is k? What is suitably large? I already have large numbers. I tried this WITHOUT k: ...
4
votes
1answer
414 views

Polar Decomposition

I'm new to Mathematica 10 (half-a-month user). I'm looking for a function of polar decomposition but for now I cannot find it. Can anyone tell me about related functions. Thanks in advance.
0
votes
0answers
165 views

Symbolic Tensor Algebra

I need to perform basic tensor algebra in order to double check some very complicated simplification. It's nothing fancy, it just has so many factors by the end that it's hard to tell if an error has ...
3
votes
0answers
85 views

Is there a way to do a symbolic PLUR decomposition of a matrix? [duplicate]

I am looking for a way to achieve the PLUR decomposition of a maitrx, as given in this paper here. The equivalent syntax in Maple is: ...
1
vote
1answer
136 views

Efficient method of raising matrix to a variable power?

I have a $2 \times 2$ matrix $A$, where each element is a 12th order polynomial in a parameter $a$. I need to raise this matrix $A$ to the $-t/T$ power, where $T$ is a known scalar (for this ...
5
votes
3answers
351 views

Multiplying block matrices

I have a 2*8 matrix A, and a 2*8*2 matrix B. So B[[1]] and B[[2]] are both 8*2 matrices. I need a neat way to multiply A by B so that the first list in the result is A.B[[1]] and the second list ...
2
votes
1answer
132 views

Anyone knows the algorithm used by NullSpace function?

NullSpace function gives a list of vectors that forms a basis for the null space of the input matrix. When the rank of the input argument matrix $M_{m\times n}$ is ...
3
votes
2answers
138 views

Eigenvectors of large symbolic matrix

I have large symbolic matrix of order 32 x 32 given as ...
1
vote
0answers
39 views

Error in NullSpace, with AlgebraicNumber entries

Consider the following 14x14 matrix, with typical entry ...
0
votes
1answer
259 views

How to put constraints on NDSolve[] solution

Assumed the following example of double pendulum by Thison (Answered by Jens): Animation of double pendulum Imagine that in the given animation(i.e. http://i.stack.imgur.com/p4TgL.gif ), the second ...
0
votes
2answers
69 views

NSolve gives {{ x -> #}}, How do I make x = #; I need to use the x value again later

I want to use: demand = {1.92, 2.07, 2.37, 2.72, 2.87}*10^6; NSolve[SetV == demand[[1]]/(Cpf (1 - χ)), χ] I want to make a vector of solutions ...
0
votes
2answers
176 views

Block matrix definition and inversion

I would like to define the following block matrix $$ A=\begin{bmatrix} H-G_1 & -G_1 & \ldots & -G_1 \\ -G_2 & H-G_2 & \ldots & -G_2 \\ \vdots & \ldots & \vdots & ...
2
votes
1answer
309 views
2
votes
2answers
144 views

Find the indexes of dependent columns

I have a fairly large singular square matrix, of size 37 and rank 35. Is there a way to get a vector with the (groups of) indexes of the columns in the original matrix that are linearly dependent? ...
3
votes
1answer
122 views

Solving simultaneous systems of linear equations

I have several systems of linear equations in matrix form, and I would like to find the $\vec{x}$ that simultaneously solves them: $$A_1\vec{x} = b_1$$ $$\vdots$$ $$A_n\vec{x} = b_n$$ Is there a ...
1
vote
1answer
152 views

Why does LyapunovSolve solve non-standard form?

LyapunovSolve[A,Q] solves the equation $A P + P A^T = Q$ for $P$ whereas the standard form (wikipedia,lecture notes, p.25, linear control systems) of the Lyapunov ...
1
vote
2answers
109 views

How to extract matrix which produces given symbolic linear combinations?

Suppose I have a column matrix $\alpha$, consisting of some symbols ...
0
votes
1answer
121 views

Mathematica Lattice Reduce Command

I'm going through a very old copy of "Mathematica: A System for Doing Mathematics by Computer" for self practice. I'm on chapter 3, and ran into the LatticeReduce ...
1
vote
1answer
49 views

Minimization problem in a subset of Complex matrices

I would like to minimize $||\mathbf{A} \rho -v||$ (where $\rho , v$ are fixed vectors) with respect to the matrix $\mathbf{A}$ elements, but with $\mathbf{A}$ in a subset of complex matrices (i.e. ...
5
votes
3answers
167 views

Missing control for depth of Inner

Working on a mechanics problem, I stumbled on something peculiar: Since Inner is a generalisation of Dot, it changes its ...
2
votes
2answers
332 views

Logarithm of a matrix in base 2?

Mathematica provides the built-in command MatrixLog, which operates on a square nonsingular matrix, but it returns the natural logarithm. How can I find the base 2 ...
2
votes
1answer
40 views

Linear function on strings using UpValues

I have two functions Sup and Sdown that take a string of letters with allowed characters ...
1
vote
0answers
113 views

Symbolic Nullspace computation in parallel

I am trying to determine the nullspace of a large symbolic matrix. The single core evolution seems to take too long. I tried Parallelize[] on the commands ...
3
votes
1answer
94 views

Graphs Plotting Discontinuous

I'm trying to plot a graph from the eigenvalues of a matrix I created. The graph shows with discontinuities in it and I was looking for some feedback. Here's the code: ...
0
votes
1answer
118 views

How large can be the dimension of a complex matrix which Mathematica can handle to find its eigenalues?

I have been working with 12 cross 12 complex matrix in Mathematica , I need to work with bigger size matrix of the dimension of the order of hundreds , I was wondering if Mathematica can handle ...
0
votes
1answer
102 views

Submatrix with linearly independent columns

What I want is the submatrix where all the linearly dependent rows have been eliminated. I tried implementing this solution, but it doesn't work in the following example: ...