All Questions
Tagged with mathematica matrices
26
questions
1
vote
1
answer
81
views
Finding the eigenvectors for a $2\times 2$ matrix
Some lecture notes I’m reading present the following matrix:
\begin{equation*}
L =
\begin{pmatrix}
0 & a \\
b & c\\
\end{pmatrix}
\end{equation*}
It then says that the dominant eigenvalue $ \...
- 163
0
votes
2
answers
97
views
Mathematica help to check a positive definite matrix
I am new to Mathematica and am trying to check if the following matrix is positive definite with the program. The answer is supposed to be yes because $x > 0$ and $y > 0$ but I don't know how to ...
- 9
1
vote
3
answers
187
views
Why is $\left( \begin{array}{cc} 1 & 1 \\ 1 & 1 \\ \end{array} \right)^0\ne1$?
Why is
$\left( \begin{array}{cc} 1 & 1 \\ 1 & 1 \\ \end{array} \right)^0=\left( \begin{array}{cc} \frac{1}{2} & \frac{1}{2} \\ \frac{1}{2} & \frac{1}{2} \\ \end{array} \right)$
...
- 9,261
0
votes
1
answer
146
views
Eigenvalues of laplacean matrix of directed graph are all non-zero when calculated in mathematica
I have a problem where I am given the incidence matrix of a directed graph, and need to calculate its Laplacean matrix and respective eigenvalues. Since it is a relatively large graph, it's reasonably ...
- 13
0
votes
0
answers
40
views
Can I substitute letters for long expressions in 5x5 matrix for Jordan decomposition?
I have a 5x5 matrix with long expressions, containing 15 variables. In Mathematica, taking Jordan decomposition of the original matrix makes no progress after one day. If I substitute 25 letters A-Z ...
- 3
0
votes
3
answers
97
views
Is $M^TM=I$ not the same as $\mathbf{v}^TM^TM\mathbf{v}=\mathbf{v}^T\mathbf{v}$???
I define a function $f[\mathbf{v}]$ as follows:
$$
f[\mathbf{v}]=\mathbf{v}^T\mathbf{v}
$$
I am now interested in a group of linear transformation $M$ ($n\times n$ matrices) which leaves the ...
- 2,589
6
votes
1
answer
2k
views
Eigenvalues of rank-$1$ update
If I have a diagonal matrix with rank-$1$ update $$D + u v^T$$ what can I say about its eigenvalues?
I know from Two matrices that are not similar have (almost) same eigenvalues that every eigenvalue ...
- 103
0
votes
1
answer
57
views
averaging two rows in a matrix with mathematica
If I have a $500 \times 500$ matrix and I would like to replace every ($5n-1$) row with the average of $(5n-1)$ and $(5n)$. How would I be able to do this with Mathematica?
- 35
0
votes
0
answers
57
views
Is it possible to block diagonalise a complex matrix with some arbitrary matrix elements?
I have a matrix of this form
\begin{bmatrix}
\ 0 & v_1 & we^{-ik} \\[0.3em]
\ v_1 & 0 & v_2 \\[0.3em]
we^{ik} & v_2 & 0
...
- 51
0
votes
1
answer
205
views
Formal expansion of matrices using Maple or Mathematica
I'd like to evaluate some powers of sum of matrices, say I would like to evaluate $\left(A+B\right)^{n}$ with $A$ and $B$ some matrices. Since I'd like to go to high order, I'd like to use Maple or ...
- 515
1
vote
2
answers
184
views
Different eigenvectors obtained with Mathematica
Suppose that we have a matrix
$$
\begin{pmatrix}
a&c\\c&b
\end{pmatrix}.
$$
The eigenvalues of this matrix are given by $\lambda_1=(a+b-D)/2$ and $\lambda_1=(a+b+D)/2$, where $D=\sqrt{(a-b)^2+...
- 17.4k
1
vote
0
answers
250
views
Minimize the number of non-zero elements of a matrix
I have a matrix A, which is huge, and all its elements are non-zero. I want to perform the operation:
$ U_1\otimes U_2 \otimes U_3...\cdot A \cdot U_1^{\dagger}\otimes U_2^{\dagger}\otimes U_3^{\...
- 191
2
votes
1
answer
476
views
Is the adjacency matrix of a given graph (OR any graphs isomorphic to a given graph) a Kronecker product, and if so what are the factors?
I have a few triangular grid graphs that I am trying to express as the direct products of smaller graphs, if possible.
...
- 23
1
vote
1
answer
140
views
Matrix solving problem
Hi there math experts.
I have the following matrix:
$$
\begin{equation}
\begin{pmatrix}
-1x & 0y & 0 & 0 & 0.004 & 0\\
-1x & -1y & 0 & 0 & 0.001 & 0
\end{...
2
votes
1
answer
2k
views
Existence of non-trivial solution of Sylvester equation.
I'm trying to solve a special case of Sylvester equation
in my case it looks like
$$A*X=X*B$$
so it can be written in form
$$A*X+X*(-B)=C$$ where C consist of all 0 items.
I tried to solve it in ...
- 181