All Questions
Tagged with applications matrices
34
questions
80
votes
4
answers
3k
views
Factorial of a matrix: what could be the use of it?
Recently on this site, the question was raised how we might define the factorial operation $\mathsf{A}!$ on a square matrix $\mathsf{A}$. The answer, perhaps unsurprisingly, involves the Gamma ...
- 3,234
4
votes
1
answer
385
views
What are practical examples of Toeplitz matrices?
A Toeplitz matrix is one in which each descending diagonal from left to right is constant. Given that structure, matrix operations are sometimes much faster. Where are Toeplitz matrices likely to ...
2
votes
1
answer
117
views
Applications where rank-1 matrices are useful
I am trying to list down applications where having a rank-1 matrix is advantageous. I know only of 2D convolution which boils down to a series of 1D convolutions if filter response is separable.
Can ...
1
vote
0
answers
182
views
Efficiency of RREF algorithms
Compute the RREF of the following matrix :$$\begin{bmatrix}1&-1&2&-3&7\\4&0&3&1&9\\2&-5&1&0&-2\\3&-2&-2&10&-12\end{bmatrix}$$
My friend ...
3
votes
2
answers
824
views
What are the units of an inverse matrix?
As the title suggests. For example if I have a matrix $A = \begin{pmatrix}
a & b\\
c& d
\end{pmatrix}$ and all elements consist of variables with units $kg$ and then I take the inverse of ...
- 165
2
votes
2
answers
626
views
Matrix expressions for the oblique projection onto subspace L in the direction of subspace K
In the past, I have had to write 3D visualization programs where, in a natural way, oblique projections onto a plane where needed. Each time, I had to develop a specific routine. Later on, I ...
- 55k
3
votes
1
answer
368
views
Applications of matrix differentiation
I know that ordinary differentiation has many real world applications, from quantum physics to economics, but I cannot think of any real world applications of matrix differentiation. So, do any real ...
5
votes
1
answer
109
views
Standard matrices to test low rank decomposition
I am working on a low rank decomposition technique that is robust to different types of noise (gaussian, salt and pepper, poisson). For starters, I simulated such low rank matrices and have ...
- 101
0
votes
1
answer
238
views
Uses for eigenvalues of unitary matrices
The eigenvalues of a unitary matrix lie on the unit circle. What are some applications in which the eigenvalue distribution of the matrix is important? For instance, that the eigenvalues are clustered,...
- 3,028
69
votes
20
answers
9k
views
What are some applications of elementary linear algebra outside of math?
I'm TAing linear algebra next quarter, and it strikes me that I only know one example of an application I can present to my students. I'm looking for applications of elementary linear algebra outside ...
- 218
5
votes
3
answers
3k
views
Are there any applications of matrices, or linear algebra to chess? If so, are there good books on it?
Chess has never had any appeal to me, but recently my brother bought a chess set, and I realized that the board can be represented as an 8x8 matrix, and each type of of piece as a number from 0 to 6, ...
3
votes
1
answer
183
views
How to get the integral of $\log(\det(A + Bt))$ w.r.t variable t?
Suppose we have two positive definite matrices $A$ and $B$, now I want to get the integral of:
\begin{align}
\int_{a}^{b} \log(\det(A + Bt)) dt ~~~~~~~~~~~~\text{for } a, b > 0
\end{align}
...
- 152k
4
votes
3
answers
1k
views
Applications of companion matrices
I'm looking for interesting applications of companion matrices. I can also use the Frobenius Normal Form.
I already covered the Cayley-Hamilton Theorem and the application to linearly recursive ...
4
votes
3
answers
12k
views
Real world situation with System of Equation with 3 variables?
Where do you run into a real world situation involving 3 variables and 3 equations? Can someone think of a specific example from business, etc? I recall taking an operations research course that ...
1
vote
1
answer
455
views
Represent a Toeplitz matrix in an array
I need to represent a $n \times n$ Toeplitz matrix in a $2n - 1$ array. I need to create a function that takes a pair $(i,j)$ and returns the value in the $2n - 1$ array.
I am having a difficult time ...