All Questions
Tagged with applications matrices
34
questions
1
vote
0
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176
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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 ...
- 4,055
3
votes
1
answer
361
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 ...
- 831
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 ...
- 151
3
votes
2
answers
819
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
0
votes
1
answer
236
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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,...
- 1,420
3
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1
answer
183
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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}
...
- 123
2
votes
2
answers
622
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 ...
- 83.8k
4
votes
8
answers
8k
views
Practical application of matrices and determinants
I have learned recently about matrices and determinants and also about the geometrical interpretations, i.e, how the matrix is used for linear transformations and how determinants tell us about area/...
1
vote
1
answer
71
views
Equations or areas where $(AA^T)^x$ or $(A^TA)^x$ are used as applications
Let $A$ be square or rectangular and $x\in \mathbb{R}$. Can you point me to equations/areas out there where $(AA^T)^x$ or $(A^TA)^x$ or their eigenvalues are used as applications? e.g. we find them in ...
- 571
2
votes
1
answer
110
views
Are there applications of equivalent matrices?
Similar to the definition here,
matrices $A$, $B$ $\in \mathbb{C}^{m\times n}$ are said to be equivalent if there exist some invertible $m\times m$ matrix $P$ and some invertible $n\times n$ matrix $Q$...
- 571
4
votes
1
answer
384
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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 ...
- 211
1
vote
1
answer
59
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Application of linear systems
A retired couple wishes to have an additional annual income of $\$6000$ per year.
As their financial consultant, you recommend that they invest some money in Treasury Bills ($t$) that yield $6$%, ...
- 467
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, ...
- 1,155
8
votes
1
answer
478
views
Why do we care about normal matrices/operators?
We know that normal operators are "nice". In the finite dimensional case, the spectral theorem tells us everything we need to know. In the infinite dimensional case, we can define a continuous ...
- 227k
1
vote
2
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846
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Applications of non-square matrices
I am wondering if non-square matrices have many applications.
It seems in my algebra classes we tend not to use them.
- 177