All Questions
Tagged with applications matrices
34
questions
1
vote
0
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182
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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
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 ...
- 780
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
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
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,...
- 1,420
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}
...
- 123
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 ...
- 83.9k
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
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 ...
- 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
480
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 ...
- 228k
1
vote
2
answers
848
views
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.
- 187
-1
votes
1
answer
75
views
An application of two 3x3 matrices identity [closed]
What is the proper context or the physical meaning for the following problem?
In particular, is it related to a classical equation?
Let $A$ and $B$ be two $3\times3$ matrices, such that $\det A=1$ ...
- 1,157
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 ...
- 997
1
vote
0
answers
32
views
The 1,1 coordinate of a Leslie matrix
I'm reading about Leslie matrices and I think I get the main idea. In the matrix, for instance,
$$ \left( \begin{matrix}
.2 & 1.1 & .5 \\
.9 & 0 & 0 \\
0 & .7 & 0
\end{...
- 5,696
80
votes
4
answers
3k
views
Factorial of a matrix: what could be the use of it?
Recently on this site, the question was raised how we might define the factorial operation $\mathsf{A}!$ on a square matrix $\mathsf{A}$. The answer, perhaps unsurprisingly, involves the Gamma ...
- 933
2
votes
0
answers
70
views
Matrix identification
Is there any name for a square, symmetric matrix, created in the following format:
$$M_{i,j} = \left\{\begin{matrix}
i + j & i \neq j\\
0 & i = j
\end{matrix}\right.$$
where $i, j$ start ...
- 2,665
1
vote
1
answer
1k
views
What are some Applications of Hermitian Positive Definite matrices?
I am learning about Hermitian positive definite matrices and the way that they can be decomposed with Cholesky decomposition. I have learned that these matrices deserve special attention for how often ...
- 4,429
-1
votes
2
answers
4k
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What are some real life applications of least squares problem?
I'm looking for some applications that require solving the least square problem.
I know polynomial fitting is one of them, but sure there are many others.
Thanks
- 440
69
votes
20
answers
9k
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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 ...
0
votes
1
answer
298
views
Matrix diagonalization example
I want a real world example or simply a good example that explains the use of a diagonal matrix, and when to prefer to use a diagonal matrix?
any other important information about diagonal matrix or ...
0
votes
0
answers
73
views
Representative value of non-square matrix
First of all, I apologise if this question is inappropriate, I wish I could be more specific - but due to the nature of it, as I am actually asking for a suggestion of some technique, that's hard to ...
- 601
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 ...
- 4,771
7
votes
1
answer
5k
views
A real life application for QR decomposition
I need to use the QR decomposition of a matrix for a real life application, (use it on a particular matrix form) and I have no idea what to do. Can you suggest me a real life application for this? ...
- 91
2
votes
1
answer
3k
views
Finding the "differentness" of two point clouds
I would like to reduce the "differentness" of two point clouds $X$ and $Y$ to a single comparable value $\lambda$, which would ideally be $0$ when $X$ and $Y$ are identical upto isometry (rotation, ...
- 121
2
votes
3
answers
23k
views
What are the applications of matrices in real world?
Matrices are considered very important in mathematics. What are some examples of applications of matrices to real world problems that would be understandable by a layman?
- 151
4
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1
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1k
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Transpose a square matrix code
I know it's not programming area , but I think it's more related to math.
I have the following function:
...
- 3,470
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 ...
- 3,470
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 ...
- 4,468
20
votes
2
answers
6k
views
Ratio of largest eigenvalue to sum of eigenvalues -- where to read about it?
Let $E_j$ be the $j$th largest-magnitude eigenvalue of a real symmetric $N \times N$ matrix $M$. I've found that the ratio
$$\frac{|E_1|}{\sum_{j=1}^N{|E_j|}},$$
is a measure of the "rank-one-ness" ...
- 201
2
votes
1
answer
1k
views
Find a price vector p for various prices of industries.
( Leontief input-output model ) Suppose that three industries are interrelated so that their outputs are used as inputs by themselves, according to the $3 \times 3$ consumption matrix
A = [$a_{jk}$...
Jasen