Questions on the linear algebra functionality of Mathematica.

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17 views

Maximizing Autoencoder Hidden Unit Function [migrated]

Given \begin{align} a = f\left(\sum_{j=1}^{100} W_j x_j \right). \end{align} where $f$ is the sigmoid function, $W$ and $x$ are $100 \times 1$ matrices with the constrain \begin{align} ||x||^2 = ...
1
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1answer
55 views

Transform linear system into a matrix form

I have a system of linear equations in variables $A_n$ of form: $$ \sum _{k=-K}^K h_k A_{n-k} J_{n-k}\left(\frac{(1-i) \text{$\eta $Sqrt}(n-k)}{\sqrt{2}}\right)+A_n\left(\frac{(1-i) \eta ...
-1
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0answers
34 views

Nonlinear eigenvalue problem

I deal with such a equation $$-y''(x) + x^2\cdot y(x) - |y(x)|^2\cdot y(x) = E y(x)$$ where E is eigenvalues with initial conditions: $y(-300) = 0$ and $y(300) = 0$. I want to figure out ...
0
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0answers
81 views

Gaussian Elimination with full pivoting [on hold]

I have some problems with an implementation of the Gaussian elimination with full pivoting. It seems to me that I've programmed it correctly, but nevertheless it throws errors and I can't find my ...
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0answers
39 views

CharacteristicPolynomial returns 0

I have the following matrix. ...
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0answers
45 views

Reordering numerically calculated eigenvalues assuming smooth dependence on a parameter

As was discussed in a different question here on SE (link) if you compute eigenvalues numerically of a matrix which depends on a parameter y, the resulting plot of ...
0
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0answers
32 views

Can LinearSolve use Parallelize and WorkingPrecision in computation

I am looking for a two things while calculating the large array matrix equation: 1) To increase the precision in simple LinearSolve[] function 2) To find a way to parallelize the computation on all ...
8
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1answer
162 views

Possible Method for MatrixExp

Well, probably a hard question, but I think it's better to cry out loud :). I noticed that MatrixExp owns Method option when ...
0
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1answer
87 views

Extract coefficient matrix $A$ from expression $f(x)$

I have expression: $$f(x)=\sum_{i=0}^{K-1}\sum_{j=0}^{N-1}a_{i,j}e^{ix}x^j.$$ I want to extract coefficient matrix $A$ from expression $f(x)$ where $$A=\left( \begin{array}{ccccc} a_{0,0}& ...
3
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1answer
107 views

$\mathbf L\mathbf D\mathbf L^\top$ Cholesky decomposition

Mathematica can do a Cholesky decomposition $\mathbf A = \mathbf L\mathbf L^\top$, but how do I do a LDL decomposition $\mathbf A = \mathbf L\mathbf D\mathbf L^\top$, with $\mathbf L$ being a unit ...
2
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1answer
58 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
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1answer
49 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 ...
2
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0answers
52 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
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3answers
192 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 ...
1
vote
1answer
68 views

Are variables always assumed to be real in Jordan Decomposition?

If you give the Input in Mathematica 9.0 (Student Edition) JordanDecomposition /@ ({{1, #}, {#, -1}} & /@ {i, I}) Mathematica gives you two completely ...
0
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0answers
20 views

Solving (one variable) Linear Equation by Dividing Slope by Constants Accumulation? [migrated]

I've been Google searching for this, and apparently my Googlefu is not strong today, or I'm doing something wrong. I have been told that it is possible to solve a one variable linear equation by first ...
3
votes
2answers
51 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? ...
1
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1answer
63 views

Eigenvectors with imaginary part

I am working on the following: ...
0
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2answers
45 views

Create a random 2x2 matrix with a repeated eigenvalue and single eigenvecor

Does anyone have a good technique for creating a random $2\times 2$ matrix that has one eigenvalue of multiplicity two, but only a single eigenvector? And more generally, has anyone written a ...
2
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2answers
166 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
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1answer
96 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 ...
3
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1answer
192 views

How to draw a tropical surface?

By definition, a tropical surface in $\mathbb R^3$ is the set of points $(x,y,z)$ where the maximum $f=max(f_1,f_2,\dots,f_n)$ is attained at least twice, here $f_i$ stand for some linear functions of ...
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0answers
68 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
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0answers
25 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
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1answer
113 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 ...
5
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3answers
406 views

Verify Cayley-Hamilton Theorem

Consider the matrix: A = {{-1, -4, -2}, {0, 1, 1}, {-6, -12, 2}} Now, the characteristic polynomial is found: ...
2
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1answer
123 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
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0answers
62 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
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1answer
65 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
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0answers
17 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
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1answer
54 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
59 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
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1answer
116 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
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0answers
62 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
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0answers
23 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
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2answers
67 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
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1answer
50 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
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1answer
79 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
215 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
73 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
43 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 ...
0
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0answers
40 views

Failure to evaluate functions of derivatives of Theta functions

I define a variant of the EllipticTheta function (multiplied by a constant factor) : ...
2
votes
1answer
109 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
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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 ...
8
votes
1answer
207 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
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0answers
96 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
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6answers
125 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
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0answers
39 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
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1answer
69 views

Why `FindMaximum` doesn't work in my example

Consider the following function ...
1
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2answers
83 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 ...