Questions on the linear algebra functionality of Mathematica.

learn more… | top users | synonyms

2
votes
1answer
61 views

Algebraic Manipulations with Indices

I am absolutely new to Mathematica, but I've heard it is a pretty powerful tool for symbolic calculations. My problem (stated generally): I have three dimensional array. I define a symbolic operator ...
4
votes
1answer
53 views

Finding maximal subset of linearly independent functions

I've got a set of functions in one variable. I wish to find the basis of the corresponding spanning set Example: $$\left\{1,\frac{1}{1-\sqrt{x}},\frac{1}{1-x},\frac{\sqrt{x}}{1-x}\right\}$$ may ...
3
votes
0answers
68 views

LinearSolve and Krylov Method options

I need to solve a large, sparse, linear system. At some point Method -> "Multifrontal" fails and a bit later also "Pardiso" ...
1
vote
3answers
206 views

Using mathematica to visualise solution of vectors and planes

Im struggling with a question I'm my math book and I wanted to use mathematica to visualise it for me, the problem is that I don't even get something remotely similar to what I was expecting. How here ...
5
votes
3answers
469 views

Verify Cayley-Hamilton Theorem

Consider the matrix: A = {{-1, -4, -2}, {0, 1, 1}, {-6, -12, 2}} Now, the characteristic polynomial is found: ...
1
vote
1answer
65 views
2
votes
1answer
103 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 ...
4
votes
2answers
63 views

Using LeviCivitaTensor

I have 2 questions about using LeviCivitaTensor, based on the following session: The signs for the cross product seems to come out "opposite" of what I expected. Why is that? Did I miss anything? ...
2
votes
2answers
177 views

Are there any good mass row/column swapping functions for matrices?

I have the following matrix Keeping the 20 row and 20 column fixed (so the 21st rows and columns because I started at 0)...how do I push each row and column back one spot? I need to push the 0th row ...
5
votes
1answer
108 views

Checking if a symbolic matrix is positive semi-definite

As far as I can tell, there is no way to tell the builtin PositiveSemidefiniteQ about assumptions on symbols. For example, the matrix ...
0
votes
0answers
75 views

Solving symbolically large system of underdetrmined linear equations

I would like to find matrices 3x3, say A, B, C, such that for all symmetric matrices X, with zero trace, one has: $$AX_1+BX_2+CX_3=0, AX_2=BX_1, AX_3=CX_1, BX_3=CX_1$$ where $X_i$ denotes i-th row (or ...
0
votes
0answers
26 views

How do I get Mathematica to evaluate symbolic linear algebra [duplicate]

First of all, I am VERY new to Mathematica. That said...I have defined vectors as: e1=2x-y and e2=x+y (x and y are orthonormal). I also defined the dot products of x and y in Mathematica. I want to ...
1
vote
1answer
125 views

Forcing solutions to avoid Root[]

I'm solving a system of ordinary non-homogeneous differential equations (4 equations). The solutions will include some algebraic equations solutions as known from text books due to the use of an eigen ...
2
votes
0answers
70 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 ...
0
votes
1answer
81 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} ...
2
votes
1answer
77 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} ...
1
vote
0answers
21 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
68 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
64 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 ...
1
vote
1answer
133 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 ...
2
votes
4answers
432 views

Selecting terms containing some expression

Imagine I have an expression like a*k + (a^2)*b*c + b*e and I would like to obtain the term containing, for example, some power of a. In that case I would ...
9
votes
1answer
216 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 ...
0
votes
0answers
75 views

Calculating the rank of an abstract matrix

I'm trying to compute the rank of a 4x4 matrix with 4 parameters and 2 variables. I tried to calculate its rank under some assumptions on those conditions and I kept getting rank 4. So I did an ...
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
72 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. ...
0
votes
1answer
88 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 ...
-1
votes
1answer
53 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 ...
2
votes
1answer
224 views
3
votes
0answers
79 views

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

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: ...
0
votes
1answer
54 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 ...
10
votes
4answers
2k views

Axis/Angle from rotation matrix

With r=RotationMatrix[a,{x,y,z}] I can compute a 3D rotation matrix from axis/angle representation. Given a 3D rotation matrix ...
0
votes
0answers
42 views

Failure to evaluate functions of derivatives of Theta functions

I define a variant of the EllipticTheta function (multiplied by a constant factor) : ...
7
votes
3answers
680 views

How to estimate the matrix condition number in the 2-Norm?

The Mathematica documentation say it is possible to estimate the Matrix condition number in norm 1, 2, Infinity. But the 2-Norm raise a message. This is an extract from reference documentation ...
1
vote
0answers
32 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 ...
1
vote
0answers
116 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
131 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
43 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 ...
0
votes
1answer
77 views
1
vote
2answers
99 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
157 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: ...
0
votes
0answers
94 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 ...
1
vote
1answer
106 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
288 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 ...
3
votes
2answers
122 views

Eigenvectors of large symbolic matrix

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

Mathematica Numeric Output

I'm using Mathematica to compute barycentric coordinates, and the output for my points is not being computed, but rather it just shows it in the form that I inputted as. For example, I have: ...
0
votes
1answer
120 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
67 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 ...
1
vote
1answer
139 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 ...
3
votes
1answer
109 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 ...