The Multistate Anti-Terrorism Information Exchange Program, also known by the acronym MATRIX, was a U.S. federally funded data mining system originally developed for the Florida Department of Law Enforcement described as a tool to identify terrorist subjects.
The system was reported to analyze government and commercial databases to find associations between suspects or to discover locations of or completely new "suspects". The database and technologies used in the system were housed by Seisint, a Florida-based company since acquired by Lexis Nexis.
The Matrix program was shut down in June 2005 after federal funding was cut in the wake of public concerns over privacy and state surveillance.
$$\langle p | W | p' \rangle = \int \langle p | x \rangle \langle x W | x' \rangle \langle x' p' \rangle dx dx'$$
$$\langle p | W | p' \rangle = \int \langle p | x \rangle \delta(x-x') W(x) \langle x' | p' \rangle dx dx'$$
$$\langle p | W | p' \rangle = \int \langle p | x' \rangle W(x') \langle...
Hi,
It's actually not a homework problem but I still decided to post it here.
Problem:
Consider Ax=y, where A is mxn and has rank m. Is (A′A)⁻¹A′y a solution? If not, under what condition will it be a solution? Is A′(AA′)⁻¹y a solution?
The given solution is:
Consider Ax=y with A mxn and...
Mentor note: Since the technique used here involves differentiation, I moved this to the Calculus section.
Hi,
I was trying to do the problem below. I was following the approach presented in this answer. I assume the approach is correct. The answer I ended up with is clearly wrong. Where am I...
Hello! I need to calculate the ABCD matrix for a thick concave mirror, in the situation in which the light comes from the plane side of the mirror, and it is the concave part that is coated (for reference, I have a Fabry Perot cavity with 2 concave mirrors, and I want to mode match the laser...
Hi,
I was trying to find the rank of following matrix.
I formed the following system and it seems like all three columns are linearly independent and hence the rank is 3. But the answer says the rank is '2'. Where am I going wrong? Thanks, in advance!
https://drive.google.com/file/d/1g7fjWAUEpOo2NukqFqZI4Wrujud6sjbn/view?usp=sharing
$\tiny{4.288.T20}$
Suppose that A is a square matrix of size n and $\alpha \in \CC$ is $\alpha$ scalar.
Prove that $\det{\alpha A} = \alpha^n\det{A}$.
Using $\alpha=5$
$\det{5A}=\det\left(5\left[...
Hi,
I have a 3 mass system. ##M \neq m##
I found the forces and I get the following matrix.
I have to find ##\omega_1 , \omega_2, \omega_3## I know I have to find the values of ##\omega## where det(A) = 0, but with a 3x3 matrix it is a nightmare. I can't find the values.
I'm wondering if...
Hello,
I am looking for a worked out solution to diagonalize a general 4x4 Hermitian matrix. Is there any book or course where the calculation is performed? If not, does this exist for the particular case of a traceless matrix? Thank you!
I have successfully found the N by N matrix corresponding to the operator R.
But the problem is, whenever I try to operate R on |bj> basis vectors, I am not getting |b(j+1)> as it should be.
Instead, I am getting result as given in the question only by <bj|R = <b(j+1)|
Matrix is not working...
Hi everyone I am new to this or any online math board community,
I’m looking for assistance in determining and calculating the size of a lottery draw pattern matrix, using simple mathematics formulas. That I myself can learn to use to include math formulas on the information pages of my new...
Trying to use <+|+>=1=<-|-> and <-|+>=0 to prove each iteration of the equation, so I have 6 different versions to prove. But the part I'm currently stuck on is understanding how to simplify any given version. I've written out [S_x,S_y]=S_xS_y\psi-S_yS_x\psi and expanded it in terms of the...
Hey! :giggle:
We have the following linear maps \begin{align*}\phi_1:\mathbb{R}^2\rightarrow \mathbb{R}, \ \begin{pmatrix}x\\ y\end{pmatrix} \mapsto \begin{pmatrix}x+y\\ x-y\end{pmatrix} \\ \phi_2:\mathbb{R}^2\rightarrow \mathbb{R}, \ \begin{pmatrix}x\\ y\end{pmatrix} \mapsto...
Hi,
suppose I am given an SL(2C) matrix of the form ##\exp(i\alpha/2 \vec{t}\cdot\vec{\sigma})## where ##\alpha## is the complex rotation angle, ##\vec{t}## the complex rotation axis and ##\vec{\sigma}## the vector of the three Pauli matrices.
I would like to decompose this vector into...
While reading the Strang textbook on tilted ellipses in the form of ax^2+2bxy +cy^2=1, I got to thinking about ellipses of the form ax^2 + 2bx + 2cxy + 2dy + ey^2=1 and wondered if I could model them through 3x3 symmetric matrices. I think I figured out something that worked for xT A x, where x...
Also, if it's possible, I would really like to know the command for inputting this kind/type of problem on Ti-89 in order to check correct answers for linear algebra problems like this one.
I'm working on the time-dependent Schrodinger equation, and come across something I don't understand regarding notation, which is not specific to TDSE but the Schrodinger formalism in general. Let's say we have a non-trivial potential. There is a stage in the development of the TDSE where we...
Matrix multiplication is defined by
\sum_{k}a_{ik}b_{kj} where ##a_{ik}## and ##b_{kj}## are entries of the matrices ##A## and ##B##. In definition of orthogonal matrix I saw
\sum_{k=1}^n a_{ki}a_{kj}=\delta_{ij}
This is because ##A^TA=I##. How to know how many independent parameters we have in...
I think you all can see that ##a_{(i+1,j+1)} = a_{i,j} + a_{i+1,j} + a_{i,j+1}##
Now the determinant always give me problem. I have and idea to reduce this matrix by Chio to a 2x2 matrix and find the determinant of this 2x2.
Put i was not able to see any pattern to find what how the 2x2 matrix...
Hello,
I am studying change of basis in linear algebra and I have trouble figuring what my result should look like.
From what I understand, I need to express the "coordinates" of matrix ##A## with respect to the basis given in ##S##, and I can easily see that ##A = -A_1 + A_2 - A_3 + 3A_4##...
I'm reading the book QFT by Ryder, in the section where ##\rm{SU(2)}## is discussed.
First, he considered the group of ##2 \times 2## unitary matrices ##U## with unit determinant such that it has the form,
$$U =\begin{bmatrix}
a & b \\
-b^* & a^*
\end{bmatrix}, \qquad \xi =
\begin{bmatrix}...
Summary:: I am suppose to show that this columns matrix does not transform as a vector. In another words, it is not in fact a vector.
I think this become trivial if we get the rotation matrix composed of Euler angles. But, i think that it is not the best way to solve this problem, and i...
$\tiny{311.2.2.6}$
Use the inverse to solve the system
$\begin{array}{rrrrr}
7x_1&+3x_2&=-9\\
-2x_1&+x_2&=10
\end{array}$
the thing I could not get here without a calculator is $A^{-1}$
What's the correct command for finding an LU factorization of a 3x3 and 4x4 matrix on Ti-89 graphing calculator? I'm trying to find the correct answers and verify/check my answers for Linear Algebra problems.
With ##\rho=\sum_i p_i|\Psi_i\rangle\langle\Psi_i|##If the ##p_i=|\langle\Psi|\lambda_i\rangle|^2## are taken as joint probabilities given by quantum mechanics for the singlet state in EPRB then this cannot represent a statistical mix (classical) of those states because of Bell's theorem ?
But I actually don't get the same matrix. What I get is the transpose of the other when I change the order
i.e when I do [A]^2[A] I get the transpose of [A][A]^2 and vice versa
What I'm trying to do is find the cube of the expectation value of x in the harmonic oscillator in matrix form.
We're...
Hey! 😊
Calculate the Cholesky decomposition of the matrix, the only non-vanishing elements are the diagonals $1,2,3, \lambda$ and all under and upper secondary diagonal elements are $1$.
For which $\lambda$ is the matrix singular?
Could you please explain the form of the Matrix?
Does the...
I have solved the exercise, so I'm not giving the vectors explicitly. I just want to know if there is a quicker way than mine.
We know that ##A## must have ##4## columns and ##4## lines, and we also know that its nullity is ##2##, thus its rank is ##2##.
I took the simplest matrix that can have...
Be ##T_{1}, T_{2}## upper and lower matrix, respectivelly. Show that we haven't matrix ##M(NxN)## such that ##M(NxN) = T_{1}\bigoplus T_{2}##
I am not sure if i get what the statement is talking about, can't we call ##T_{1},T_{2} = 0##? Where 0 is the matrix (NxN) with zeros on all its entries...
There is no specific example but my attempt at one would be to make the non-symmetric matrix symmetric. Then we would be able the usual formulas as designed for symmetric matrices. Is this how it works?
Alternatively, do I just calculate the Eigen values without making it symmetric? I don't...
I need to find the matrix transformation of y = \frac{1}{x} onto y = \frac{-1}{3x-1}-2
I think its
\begin{bmatrix}
x'\\
y'
\end{bmatrix}
=\begin{bmatrix}
3 & 0 \\
0 & -1
\end{bmatrix}
\begin{bmatrix}
x\\
y
\end{bmatrix}
+
\begin{bmatrix}
-1\\
-2
\end{bmatrix}
is is possible to multiply the matrix M with either A or c->?
And if i have to write the matrices in this form: , do i divide c-> by A or do i follow som other formula?
The basis he is talking about: {1,x,x²,x³,...}
I don't know how to answer this question, the only difference i can see between this hermitians and the others we normally see, it is that X is acting on an infinite space, and, since one of the rules involving Hermitian fell into decline in the...
Given that the normal vector cross product is rotational invariant, that is $$\mathbf R(a\times b) = (\mathbf R a)\times(\mathbf R b),$$ where ##a, b \in \mathbb{R}^3## are two arbitrary (column) vectors and ##\mathbf R## is a 3x3 rotation matrix, and given the cross product matrix operator...
Indeed, if we take a vector field which dual to the covector field formed by the gradient from a quadratic interval of an 8-dimensional space with a Euclidean metric, then the Lie algebra of linear vector fields orthogonal (in neutral metric) to this vector field is isomorphic to the...
Hi, I have been having some trouble in finding the determinant of matrix A in this Q
Which relevant determinant property should I make use of to help me find the determinant of matrix A and maybe matrix B also
This is what I have tried for matrix A so far but it's not much help really
Any...
I'd like to show that, by minimizing this functional
$$\Omega[\hat \rho] = \text{Tr} \hat \rho \left[ \hat H - \mu \hat N + \frac 1 {\beta} \log \hat \rho \right]$$
I get the well known expression
$$\Omega[\hat \rho_0] = - \frac 1 {\beta} \log \text{Tr} e^{-\beta (\hat H - \mu \hat N )}$$
I'm...
If I have a matrix representing a 2nd order tensor (2 2) and I want to convert this matrix from M$$\textsuperscript{ab}$$ to $$M\textsubscript{b}\textsuperscript{a}$$ what do I do? I'm given the matrix elements for the 2x2 tensor. When applying the metric tensor to this matrix I understand...
I have 2 Fisher matrixes which represent information for the same variables (I mean columns/rows are the same in the 2 matrixes).
Now I would like to make the cross synthesis of these 2 matrixes by applying for each parameter the well known formula (coming from Maximum Likelihood Estimator...
So let's say that we have som unitary matrix, ##S##. Let that unitary matrix be the scattering matrix in quantum mechanics or the "S-matrix".
Now we all know that it can be defined in the following way:
$$\psi(x) = Ae^{ipx} + Be^{-ipx}, x<<0$$ and $$ \psi(x) = Ce^{ipx} + De^{-ipx}$$.
Now, A and...
In a certain anisotropic conductive material, the relationship between the current density ##\vec j## and
the electric field ##\vec E## is given by: ##\vec j = \sigma_0\vec E + \sigma_1\vec n(\vec n\cdot\vec E)## where ##\vec n## is a constant unit vector.
i) Calculate the angle between the...
The note I get from the teacher states that for transition matrix, the column part will be current state and the row part will be future state (let this be matrix A) so the sum of each column must be equal to 1. But I read from another source, the row part is the current state and the column...
Starting from the definition of a matrix exponential as a power series, how would we show that ##(e^A)^n=e^{nA}##?
I know how to show that if A and B commute then ##e^Ae^B = e^{A+B}## and from this we can show that the first identity is true for integer values of n, but how can we show it’s...
In Rigid body rotation, we need only 3 parameters to make a body rotate in any orientation. So to define a rotation matrix in 3d space we only need 3 parameters and we must have 6 constraint equation (6+3=9 no of elements in rotation matrix)
My doubt is if orthogonality conditions...