For any topic related to matrices. This includes: systems of linear equations, eigenvalues and eigenvectors (diagonalization, triangularization), determinant, trace, characteristic polynomial, adjugate, transpose, Jordan normal form, matrix algorithms (e.g. LU, Gauss elimination, SVD, QR), ...

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1
vote
0answers
23 views

Solving tridiagonal matrices where the top left element is zero

If I have a matrix like this: $$ \left[\begin{array}{rrrrrrrrr|r} 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 1 & 1 & 0 & 0 & 0 & 0 & ...
1
vote
1answer
28 views

Express summation in terms of matrix norm

Express the following $$\sum _{ i=1 }^{ n }{ ({ \beta }_{ 1 }x_{ i }+{ \beta }_{ 0 }-y_{ i })^{ 2 } }$$ To become something of the form: $∥Ax−b∥^{ 2 }$ where $A$ is an $m$−by−$n$ matrix and $b$ is ...
0
votes
1answer
28 views

Matrix transpose times itself

We define A to be a matrix in $R^{m*n}$ Does $A^TA$ have any particular structure? When is $A^TA$ invertible?
-7
votes
0answers
21 views

How to check the availability of particular function [closed]

I want to check the availability of particular function that returns the value of results in binary like 0 or 1....How to check these function using mathematics...
1
vote
1answer
31 views

Find the Jacobian of F

Given that $A \in \mathbb{R}^{m\times n}$, and $b \in \mathbb{R}^{m}$, we define: $$F:\mathbb{R}^{n} \rightarrow \mathbb{R} = \left\| Ax-b \right\|^2$$ Find the Jacobian of $F$, and show that it is of ...
1
vote
1answer
27 views

Reduced Row Echelon form without scalar multiplication?

Is it possible to transform any matrix to row reduced echelon form without using the row operation that multiplies a row by a scalar?
0
votes
1answer
13 views

Determine if matrix D belongs to Vect(A,B,C)

So there are 4 matrices, A, B,C,D. They belong to field F5. Determine if D belongs to Vect(A,B,C). I have pretty much done all the calculations its just i fail to conclude/find the right value for the ...
4
votes
1answer
58 views

What is the name of the matrix that is created by a vector times its transpose.

I am looking for the name of the matrix created by the following operation: $Z = z*z^T$ I know it should create a symmetric matrix with an element $Z_{ij} = z_{i}z_{j}$
2
votes
0answers
39 views

Probability that a random integer matrix is singular

Let A be a nxn-matrix with integers in the range $u..v$ , where $u<v$ are arbitary integers. Is there a formula, or at least, a good estimate, for the probability that the matrix is singular ? ...
0
votes
0answers
14 views

Numerical solution of first order ODE

I have an in-homogeneous ODE. $R'(x)-(C_1 +C_2 x) R(x) = R_1-C_1 R_0\, x \tag 1$. What I know is the constant matrix $ R(0)$ as initial condition. Question:- how to find out R(1) by numerical ...
4
votes
0answers
69 views

Minimum and maximum determinant of a sudoku-matrix

Let $A$ be a sudoku-matrix. Assume that its determinant is positive. What is the lowest, what the highest possible value for the determinant of $A$ ? $A$ must have the dominant eigenvalue $45$, but ...
1
vote
2answers
40 views

Matrix Semi-Definite Inequality [duplicate]

Does the following inequality hold? If matrix $A$ is a $n \times n $ positive semi-definite, $A \succeq 0$, and $U$ is one $n \times k$ unit column-orthogonal matrix ($k \leq n$), $U^{T}U=I$, do we ...
0
votes
3answers
25 views

Generating a Triangular Matrix via a Vector MATLAB

How do I generate an arbitrary (size n) triangular matrix with a vector? For example: A=[1;2;3;4;5;6;7;8;9;10]; And the answer should be: B=[1,2,3,4; 0,5,6,7; 0,0,8,9; 0,0,0,10] or ...
2
votes
2answers
31 views

diagonalization of a matrix over finite fields

I'm having a problem with determine whether a matrix is diagonalizable over $\mathbb F_{2}$, over $\mathbb F_{3}$, etc. for example, for the following matrix: $$ \begin{bmatrix} 1 ...
1
vote
1answer
55 views

To find the volume of the region that is bordered by 4 points in 3D space

To find the volume of the region that in the points $A(x_1,y_1,z_1),B(x_2,y_2,z_2),C(x_3,y_3,z_3),D(x_0,y_0,z_0)$. Let's define a 4X4 matrix to determine plane equation that are on $A,B,C$ ...
0
votes
2answers
53 views

string function

Jane loves string more than anything. She made a function related to the string some days ago and forgot about it. She is now confused about calculating the value of this function. She has a string ...
-5
votes
0answers
16 views

lower triangular matrix [closed]

how to retrive lower triangular matrix where the values of matrix is stored in the form of array.(only non zero elements are stored in array nad you have row index and column index)) example: values ...
0
votes
0answers
18 views

Heaviside Expansion Theorem with matrices

Is the Heaviside Expansion Theorem (HE) for the determination of inverse Laplace Transforms true for matrix expressions such that $\mathscr{L}^{-1}[\mathbf{P}(s)\mathbf{Q}^{-1}(s)] = \sum_i^n ...
0
votes
3answers
25 views

How do you know that rows are independent and what are the 120 terms?

I am having trouble with the question below, help me out;
0
votes
0answers
27 views

Eigenvalue bounds for a positive semidefinite matrix

I have a symmetric $(p\times p)$, positive semi definite matrix $\Omega$. If somebody says: find the eigenvalue bounds of the matrix such that $$w_1I \le \Omega \le w_2I$$ where $I$ is the identity ...
2
votes
0answers
42 views

Top bound on the value of an algebraic adjunct to elements of a nonnegative irreducible matrix

Let $A = ||a_{i j}||_1^n$ be nonnegative irreducible matrix with maximum eigenvalue $r$. Let $A_{i j}(\lambda)$ be an algebraic adjunct for the element $\lambda \delta_{i j} - a_{i j}$ in determinant ...
0
votes
2answers
55 views

Suppose $(x,y,z)$, $(1,1,0)$, and $(1,2,1)$ lie on a plane through the origin.

What determinant is zero? What equation does this give for the plane? I need some help here, am pretty stuck
1
vote
1answer
37 views

Find the matrix $A$ of $T$ with respect to the basis $\{1, x, x^2\}$ in both the domain and the codomain

$T : V \to V$ be defined by $T(p(x)) = p(0) + p(1)x$. Any hints on this one?
-2
votes
0answers
43 views

3D reconstruction from 2 images with baseline and single camera calibration

first posted: http://stackoverflow.com/q/24852151/3858076 i was forwarded to here cause this is more a mathematical problem so if anyone here could help me i would be very thankful. plz ignore the ...
2
votes
1answer
44 views

Let $A$ be an $n \times n$ matrix with real entries. [closed]

Which of the following is correct? (a) if $A^2=0$, then $A$ is diagonalisable over complex numbers (b) if $A^2=I$, then $A$ is diagonalisable over real numbers (c) if $A^2=A$, then $A$ is ...
1
vote
1answer
28 views

Equality case in the Frobenius rank inequality

In many linear algebra books, the following rank inequalities are found: Frobenius inequality Let $A$, $B$ and $C$ be three matrices such that the product $ABC$ is defined. Then ...
0
votes
2answers
46 views

Jordan chain when matrix has only one eigenvalue.

A $12\times 12$ matrix has sole eigenvalue $3$. It is given that the kernels of $A-3I$, $(A-3I)^{2}$, $(A-3I)^{3}$ and $(A-3I)^{4}$ have dimensions $4$, $7$, $9$ and $10$ respectively. What ...
0
votes
1answer
32 views

Equality in the Collatz-Wielandt-formula

Let A be a matrix with positive entries. The perron-frobenius-theorem states that A has a positive dominating simple eigenvalue, called the perron-frobenius-eigenvalue. I denote it with p(A). The ...
1
vote
1answer
27 views

Find the triangular matrix and determinant.

I have a 4x4 matrix and I want to find the triangular matrix (lower half entries are zero). $$A= \begin{bmatrix} 2 & -8 & 6 & 8\\ 3 & -9 & 5 & 10\\ -3 & 0 & 1 & ...
3
votes
2answers
68 views

Matrix with all eigenvalues $0$ but not triangular?

Is the situation described in the title achievable? I am looking for a $3\times 3$ case specifically.
1
vote
1answer
29 views

Linear Algebra Question concerning the trace of a symmetric positive definite matrix.

The objective is to minimize the diagonal elements of a symmetric positive definite matrix. The expression of this matrix is a little bit nasty and its inverse is much easier to deal with. Can I claim ...
0
votes
0answers
21 views

Power iteration sequemce for a special nonnegative irreducible imprimitive matrix

Let $A \in \mathbb{R}^{n \times n}$ be nonnegative irreducible matrix with maximum positive eigenvalue equal to 1. Let's assume $A$ has $h$, $h > 1$ eigenvalues $\lambda_1, \dots, \lambda_h$ with ...
0
votes
2answers
61 views

Matrices: $AB=0 \implies A=0 \text{ or } \ B=0$

When A and B are square matrices of the same order, and O is the zero square matrix of the same order, prove or disprove:- $$AB=0 \implies A=0 \text{ or } \ B=0$$ I proved it as follows:- Assume $A ...
1
vote
0answers
41 views

diagonal of pseudoinverse of laplacian matrix

I have to find the diagonal of the pseudoinverse of a laplacian matrix evaluated on a directed and weighted graph. My laplacian is defined as: L = D - A where: D is a diagonal matrix; Di,i the sum ...
0
votes
1answer
28 views

How the Wronskian works

To prove linear independence of a set of functions, we say that given their Wronskian matrix W, Wx = 0 implies trivial solution (0,0,0,...) if the value (determinant) of the Wronskian is identically ...
0
votes
1answer
22 views

Linear Algebra - elimination and linear systems

By given this matrix: \begin{pmatrix}1&1&1&0\\2&3&k&1\\3&k&5&1\end{pmatrix} I need to find, what are the values of k the system has infinity/single/no solution. So ...
0
votes
0answers
22 views

Calculating Muliti-integral Time-Ordering operator

I am trying to solve the time-ordering operator Like this: $S(t)=\mathcal{T}e^{\int_0^tduA(u)\int_0^udvB(v)}S(0)$. How can I calculate S(t) with minimum error?
0
votes
1answer
22 views

What's the correct notation for a minimum of a row of a matrix?

Let I=1,...,m denote the indexes of the rows of a matrix A Let J=1,...,n denote the indexes of the columns of a matrix A Let xi,j denote the value of the element A[i,j] I need do use a notation to ...
5
votes
7answers
188 views

If $A^2 = B^2$, then $A=B$ or $A=-B$

Let $A_{n\times n},B_{n\times n}$ be square matrices with $n \geq 2$. If $A^2 = B^2$, then $A=B$ or $A=-B$. This is wrong but I don't see why. Do you have any counterexample?
1
vote
2answers
33 views

Matrix Algebra, Signs of solution

I have a system $AX = B$, where $A$, $B$ and $X$ are $N \times N$ matrices. I am interested in the properties of the solution $X$. $B$ has the following property: the diagonal terms are strictly ...
0
votes
0answers
25 views

Find the angle of rotation about a vector caused by application of a rotation matrix

I have a rotation matrix $R$ and a unit vector $\mathbf{v}$. How can I find the angle of rotation about $\mathbf{v}$ caused by the application of $R$?
0
votes
1answer
21 views

A question in matrix theory, SVD related.

For four $m\times n$ matrices A, B, A', B'. If $AA^\dagger=A'A'^\dagger, BB^\dagger=B'B'^\dagger$ and $AB^\dagger=A'B'^\dagger$, then if there always exists an unitary matrix V in U(n) such that ...
0
votes
0answers
10 views

Matrix puzzle-Symmetric and skew symmetric matrices

Let P be an odd prime no. and T(P) be the following set of 2*2 matrices: T(p)={A=[a b] ; a,b,c belong to {0,1,2...,P-1} [c a] 1)Find the no. of A in T(P) such that A is either symmetric ...
0
votes
0answers
20 views

Homography between known and unknown rectangle corners

I would like to know if there is a solution for the problem of homography estimation in the special case in which one of the views is unknown but has some constraints, particularly if we know the ...
0
votes
1answer
55 views

Norm of a Vector

Suppose $A\inℝ^{n,n}$. We Define $$ \|A\| = \underset{\|x\| = 1}{\sup} \frac {\|Ax\|} {\|x\|}$$ Show it is a norm. Any thoughts?
2
votes
0answers
29 views

Counting symmetric binary matrices with constant line-sum

I'm trying to count, as the title suggests, symmetric matrices with entries $0$ or $1$ and constant line-sum $k$. ($0 \leq k \leq n$). If you start listing the number of these on a table you'll get a ...
0
votes
1answer
26 views

Find the matrix of T with respect to the standard basis in both the domain and the codomain

Let $T:\mathbb{R}^2→\mathbb{R}^2$ be given by $T((x,y)) = (x+2y , 3x-y)$ Question is what title states, Please help with detail.
2
votes
1answer
47 views

interger matrix whose square is identity

how can we find all the matrices with integer entries of size $n \times n$ such that $A^{2}=I$ and the matrix does not have fixed point in $\mathbb{Z}^n$ (except zero of course)? $-I$ is one example. ...
-1
votes
2answers
48 views

Matrix with eigen values given find [closed]

Let$$ P=\begin{bmatrix} 0&-2&-3 \\ -1&1 &-1 \\ a&2 &b \end{bmatrix},$$ for some $a,b \in \mathbb{R}.$ Suppose that $1$ and $2$ are eigenvalues of $P$ and $$ ...
2
votes
1answer
30 views

Strange matrix multiplication behavior in Matlab

I noticed strange behavior of some calculations in Matlab. Matlab code listing: ...