Questions on the linear algebra functionality of Mathematica.

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3answers
44 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
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1answer
58 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
49 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
60 views

Eigenvectors with imaginary part

I am working on the following: ...
0
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0answers
18 views

Applied Linear Algebra | Linear Dependent Matrix [migrated]

My response: Am I correct in my approach? Thank you for your help.
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0answers
15 views

Applied Linear Algebra | Prove the intersection of two subspaces [migrated]

Question: Determine whether or not any column in the matrix is a linear combination of other columns. Provide a general method for answering the same question for any n x n matrix A. My response: ...
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0answers
56 views

How speed the calculatation of the inverse of an upper triangular matrix

I have found the inverse of an upper triangular matrix by substitution using the "for" command, but it works very slowly when the upper triangular matrix is big. Example: If 686 is matrix's ...
0
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2answers
41 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
163 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 ...
4
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1answer
88 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
182 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 ...
0
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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
107 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
votes
3answers
344 views

Verify Cayley-Hamilton Theorem

Consider the matrix: A = {{-1, -4, -2}, {0, 1, 1}, {-6, -12, 2}} Now, the characteristic polynomial is found: ...
0
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0answers
5 views

Basis of a basis-linear algebra? [migrated]

Usually when we say that v1 and v2 are basis we imply that they are linearly independent and span the space. We by default denote v1 and v2 in i-j basis. Then how is i-j basis defined in the first ...
2
votes
1answer
122 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
57 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
58 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} ...
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0answers
16 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
47 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
56 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
107 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
55 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
22 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
66 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. ...
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1answer
48 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
73 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
209 views

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

I have two matrixes with values differs only slightly ...
0
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1answer
72 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
38 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 ...
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0answers
38 views

Failure to evaluate functions of derivatives of Theta functions

I define a variant of the EllipticTheta function (multiplied by a constant factor) : ...
2
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1answer
101 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
31 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
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1answer
204 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
83 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
121 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
37 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
67 views

Why `FindMaximum` doesn't work in my example

Consider the following function ...
1
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2answers
78 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
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2answers
152 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
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0answers
84 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
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0answers
75 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: ...
1
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1answer
89 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
273 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
97 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
109 views

Eigenvectors of large symbolic matrix

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

Error in NullSpace, with AlgebraicNumber entries

Consider the following 14x14 matrix, with typical entry ...
0
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0answers
52 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: ...