1. ### Finding expectation value of two operators in a 3 state QM system

Hi guys, I'm trying to work out the expectation values of matrix operators A and B in a system with state ##U(T)=\begin{pmatrix} c_1 e^-\frac{iE_1t}{ħ}\\ c_2e^-\frac{iE_2t}{ħ}\\ c_3e^-\frac{iE_3t}{ħ}\\ \end{pmatrix}##. So in order to get to this stage so far I used the relation...
2. ### I Proof concerning the Four Fundamental Spaces

Hello all, I am currently working on the four fundamental spaces of a matrix. I have a question about the orthogonality of the row space to the null space column space to the left null space ------------------------------------------------ In the book of G. Strang there is this nice picture...
3. ### I Determine the limit in a Markov process over time

I have already in a previous task shown that A is not irreducible and not regular, which I think is correct. I don't know if I can use that fact here in some way. I guess one way of solving this problem could be to find all eigenvalues, eigenvectors and diagonalize but that is a lot of work and...
4. ### I Finite fields, irreducible polynomial and minimal polynomial theorem

I thought i understood the theorem below: i) If A is a matrix in ##M_n(k)## and the minimal polynomial of A is irreducible, then ##K = \{p(A): p (x) \in k [x]\}## is a finite field Then this example came up: The polynomial ##q(x) = x^2 + 1## is irreducible over the real numbers and the matrix...
5. ### I Calculating A^2 where k = Z_2

In my book no explanation for this concept is given and i can't find anything about it when I am searching. One example that was given was: Let $$A=\begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix}$$ with ##k=\mathbb{Z}_2## I think k is the set of scalars for a vector that can be multiplied with...
6. ### I Is there any matrix equivalent for the Clifford product?

Well, the question is in the title.
7. ### I What is the proper matrix product?

It says in any textbook (for example, in classical text «Theory of matrices» by P. Lankaster) on matrix theory that matrices form an algebra with the following obvious operations: 1) matrix addition; 2) multiplication by the undelying field elements; 3) matrix multiplication. Is the last one...
8. ### Matrix concept Questions (invertibility, det, linear dependence, span)

I have a trouble showing proofs for matrix problems. I would like to know how A is invertible -> det(A) not 0 -> A is linearly independent -> Column of A spans the matrix holds for square matrix A. It would be great if you can show how one leads to another with examples! :) Thanks for helping...

Summary
10. ### Modeling the populations of foxes and rabbits given a baseline

From solving the characteristic equations, I got that ##\lambda = 0.5 \pm 1.5i##. Since using either value yields the same answer, let ##\lambda = 0.5 - 1.5i##. Then from solving the system for the eigenvector, I get that the eigenvector is ##{i}\choose{1.5}##. Hence the complex solution is...
11. ### Which statements are true given a solution to the system x'=Ax?

Summary:: Suppose that [x, y] = e^{-3t} [-2, -1] is a solution to the system $x' = Ax$, where A is a matrix with constant entries. Which of the following must be true? a. -3 is an eigenvalue of A. b. [4, 2] is an eigenvector of A. c. The trajectory of this solution in the phase plane with axes...
12. ### Find the sampling matrix and sampling structure for R, G and B components

Hello, everyone. :) All I could gather is that, if I'm correct, lattices are spans of the column vectors of the matrix within the "LAT()" notation and the X and Y occurrences are unit placeholders (such as the pixel unit (since this is in the context of image processing)). And, as an attempt...
13. ### Condition for AB+A+B=0 where A and B are matrices

I first tried by assuming the matrices but it was becoming complicated so i tried taking transpose on both sides,it also did not help.So now i could not think of what to do further.Help please.
14. ### I'm getting garbage values while reading matrices from a file

Hi All, While trying to read a matrix from data file using fortran90 code ,I get garbage values and a backtrace error. Error termination. Backtrace: #0 0x7f4a4de3631a #1 0x7f4a4de36ec5 #2 0x7f4a4de3768d #3 0x7f4a4dfa4d42 #4 0x7f4a4dfa6ad5 #5 0x7f4a4dfa80f9 #6 0x56040bbeae57 #7...
15. ### A tricky matrix problem?

he is asking for the division of the two matrices , so i tried to get the inverse of the matrix A but it appears to get more complex as the delta for A is somehow a big equation . and what really bothers me that there is another A , B inside the matrix B ?! find B/A .
16. ### Comp Sci How do you read two files in the same program in C++?

My matrix text files can vary from 1x1 to 10x10 (Another file will be given when the code gets tested but it's all square matrices) I'm stuck here. #include <iostream> #include <fstream> #include <string> using namespace std; int main() { const int MAXI = 10; int x, y, z...

24. ### Computer Graphics & More

Hello, I am having trouble comprehending how grids are made and defined in computers. What is the unit that they use and how is it defined ? I know that softwares use standardized units of measure (measurement) such as centimetre. Basically, how is a 3-Dimensional Space created in computers...
25. ### Matrix help — Solve this matrix equation

Homework Statement Homework Equations The Attempt at a Solution I know I would have to do something with my calculator and I tried to solve like solving an equation for C, but not sure. I put all the matrices in my calculator. I then subtracted the first matrix to the other side then...
26. ### Setting up a matrix from a linear equation

Homework Statement I need some help with a question on my assignment. It asks to set up a matrix from the linear equations, y=25x+70 and y=35x+40. Homework Equations How do I set this matrix up? The Attempt at a Solution I think that I have to rewrite it as 25x-y=-70 and 35x-y=-40. But then...
27. ### Spin component matrices

Homework Statement I'm trying to show the Eigenstate of S2 is 2ħ^2 given the matrix representations for Sx, Sy and Sz for a spin 1 particle Homework Equations Sx = ħ/√2 * \begin{pmatrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{pmatrix} Sy = ħ/√2 * \begin{pmatrix} 0 & -i & 0 \\ i & 0 & -i...
28. ### Time Derivative of Rank 2 Tensor Determinant

Homework Statement Show that for a second order cartesian tensor A, assumed invertible and dependent on t, the following holds: ## \frac{d}{dt} det(A) = det(a) Tr(A^{-1}\frac{dA}{dt}) ## Homework Equations ## det(a) = \frac{1}{6} \epsilon_{ijk} \epsilon_{lmn} A_{il}A_{jm}A_{kn} ## The...
29. ### I Adding a matrix and a scalar.

So, I recently came across this example: let us "define" a function as ƒ(x)=-x3-2x -3. If given a matrix A, compute ƒ(A). The soution proceedes in finding -A3-2A-3I where I is the multiplicative identity matrix. Now , I understand that you can't add a scalar and a matrix, so the way I see it is...
30. ### Is the zero Matrix a vector space?

Homework Statement So I have these two Matrices: M = \begin{pmatrix} a & -a-b \\ 0 & a \\ \end{pmatrix} and N = \begin{pmatrix} c & 0 \\ d & -c \\ \end{pmatrix} Where a,b,c,d ∈ ℝ Find a base for M, N, M +N and M ∩ N. Homework Equations I know the 8 axioms about the vector spaces. The...