Matrices Definition and 1000 Threads

Hi all, I make some exercises in particle physics but I'm stuck in two problems related to Gamma matrices identities, First: the Fermion propagator ## \frac {i } { /\!\!\!p - m} = i \frac { /\!\!\!p + m } { p^2 - m^2} ## So how ##/ \!\!\!\!p ^2 = p^2 ## ? Where ## /\!\!\!p = \gamma_\mu p^\mu...

Homework Statement For an arbitrary positive integer ##n##, give a ##2n## x ##2n## matrix ##A## without real eigenvalues. Homework EquationsThe Attempt at a Solution First of all, I am having some trouble interpreting this problem. I do not know if it is generalized where I am supposed to find...

What are some examples of writing matrices in the Gummi latex editor? Something about the syntax used on the forum doesn't work for me when used in Gummi.

I'm trying to show that any unitary matrix may be written in the form \begin{pmatrix}e^{i\alpha_1}\cos{\theta} & -e^{i\alpha_2}\sin{\theta}\\ e^{i\alpha_3}\sin{\theta} & e^{i\alpha_4}\cos{\theta}\end{pmatrix} Writing the general form of a unitary matrix as U=\begin{pmatrix} u_{11} & u_{12}\\...

Homework Statement Find all orthogonal 3x3 matrices of the form \begin{array}{cc} a & b & 0 \\ c & d & 1\\ e & f & 0 \\\end{array} Homework Equations There are many properties of an orthogonal matrix. The one I chose to use is: An n x n matrix is an orthogonal matrix IFF $$A^{T}A = I$$. That...

I don't quite follow this, can anyone explain?

Hi, How would you solve a singular matrix? ie when determinant is zero. Lets assume an equation, (1) Ax+By=E and (2) Cx+Dy=F if the determinant; AD-BC = 0, and therefore the matrix is singular, How to go around solving the equation? LU decomposition, Gaussian elimination? Ideally I am...

Homework Statement Consider the set of operations in the plane that includes rotations by an angle about the origin and reflections about an axis through the origin. Find a matrix representation in terms of 2x2 matrices of the group of transformations (rotations plus reflections) that leaves...

Homework Statement Show that the members of the Lie algebra of SO(n) are anti-symmetric nxn matrices. To start, assume that the nxn orthogonal matrix R which is an element of SO(n) depends on a single parameter t. Then differentiate the expression: R.RT= I with respect to the parameter t...

Hi I am now filling in what I perceive to be gaps in my knowledge. One of these problems is understanding why matrices can solve systems of equations. I do completely get Gaussian elimination to solve systems of linear equations. However, when using determinants and the like to solve, for...

Homework Statement The question arises from this quote from wikipedia's article about kronecker product: Kronecker sums appear naturally in physics when considering ensembles of non-interacting systems. Let Hi be the Hamiltonian of the i-th such system. Then the total Hamiltonian of the...

I do not have any work to show as I am not skilled enough to solve this problem as of yet. I really do need an answer to the question though. I know this is a long shot but I am desperate at the moment, so please do provide the solution with steps to the problem below. Many thanks. Problem)...

Hey guys, So consider the following product of matrices: (p_{1}^{\mu}\cdot p_{1}^{\prime\nu} -(p_{1}\cdot p_{1}')\eta^{\mu\nu}+p_{1}^{\nu}p_{1}^{\prime\mu})(p_{2\mu}p_{2\nu}'-(p_{2}\cdot p_{2}')\eta_{\mu\nu}+p_{2\nu}p_{2\mu}') where eta is the Minkowski metric. I keep getting 2(p_{1}\cdot...

Hi there, I've got a unit vector u^, arbitrary vector v, and a vector w which is the reflection of v in a line in the direction of u. I have already proved that w= 2 (u^.v)u^ - v. However, the next part of my question asks me to write w= Rv and find the components of the matrix R, taking the...

Homework Statement What is the relation between the image of A and the image of A2 + A? Homework EquationsThe Attempt at a Solution im (A^2 + A) for x (A^2+A) is within the image. Linear combination properties show A^2 x + A x. Not sure where to go from here

Homework Statement Consider a 2x2 matrix A with A2=A. If vector w is in the image of A, what is the relationship between w and Aw? Homework Equations Linear transformation T(x)=Ax Image of a matrix is the span of its column vectors The Attempt at a Solution I know that vector w is one of the...

I am reading Kristopher Tapp's book: Matrix Groups for Undergraduates. I am currently focussed on and studying Section 1 in Chapter2, namely: "1. Complex Matrices as Real Matrices".I need help in fully understanding the proof of Tapp's Proposition 2.2. Proposition 2.2 and its proof read as...

I am reading Kristopher Tapp's book: Matrix Groups for Undergraduates. I am currently focussed on and studying Section 1 in Chapter2, namely: "1. Complex Matrices as Real Matrices".I need help in fully understanding what Tapp is saying in this section regarding the function $$ \rho_n \ : \...

Homework Statement Suppose that A is an m x n matrix and there exists n x m matrices C and D such that CA=In and AD=Im. Prove that C=D Homework EquationsThe Attempt at a Solution Im not sure if I'm on the right path here. However my initial thought is that since the matrices are not square...

I want to learn clifford and grassmannian algebras. I need to be taken from mostly a beginners point, and from a place of matrices only in general terms, and years since use. ANybody up for it? I am a software developer, so not at the bottom of any learning curve.

When I am dealing with matrices and the question says compute: $4A +B$ (where $A$ and $B$ are some matrices..) should I assume that they are implying I use the normal mathematical order of operations or is it different? For example should I assume they are saying $(4*A) + B$ or $4(A+B)$

So I'm studying norm of matrices in my calc class, and most resources I've looked at seem like it's just the square root of all the entry values over the sum of all the entries, but when given the matrix [1 3] [0 1] Sqrt((11+sqrt(117))/2) The 11 is the sqrt of 12 + 32 + 12 the 2 is the root...

hi, I'm currently really struggling with an assignment that I've been tasked with. https://ss1002.files.wordpress.com/2015/01/assignment.pdf It's mostly theoretical proof questions, which I find difficult. Actual questions I'm fine with. I have done the first question without issue, as...

How we cannot apply row and column operation simultaneously on matrix when finding its inverse by elementary transformation but can apply it in determinant? I think kernel and image gets disturbed in a matrix, though I don't know what it actually is. Why not in determinant case?

Hello all, I'm trying to work on this problem for my homework, but I just can't seem to understand what to do. I know how to calculate the inversive of a matrix but I just don't know how to approach this kind of a problem. I was searching everywhere for some guidance on how to approach it...

A jar contains nickels, dimes and quarters. There are 1469 coins in the jar totaling $191.25. Assuming that the number of dimes is exactly twice that of the number of nickels, how many (each) nickels, dimes and quarters are there in the jar?We were suppose to be using matrices to solve this, it...

Homework Statement Find all 2x2 matrices X such that AX=XA for all 2x2 matricesThe Attempt at a Solution Let A = a b c d and X = w x y z Then AX = XA ==> aw+by=wa+xc ...(1) ax+bz=wb+xd ...(2) cw+dy=ya+zc ...(3) cx+dz=yb+zd ...(4) (1) ==> by = xc, which holds for all b and c only...

Homework Statement [Imgur](http://i.imgur.com/VFT1haQ.png) Homework Equations reflection matrix = 2*projection matrix - Identity matrix The Attempt at a Solution Using the above equation, I get that B is the projection matrix and E is the reflection matrix. Can someone please verify if this...

We are given the vectors la> = (1,0) and lb> = (0,1) and then a Hamiltonian H which is a 2x2 matrix with 2 on the diagonal entires and zero elsewhere. I am asked to now represent H in the basis of the vectors la'> = 1/sqrt(2)(1,1) and lb'> = 1/sqrt(2)(1,-1), which are also eigenvectors of H...

Can anyone explain to me what is the cofactor matrix? I have trouble finding on the net the intuition behind it. Likewise what is the meaning of the adjugate matrix?

My professor gave us this problem and said its a trick question. I think I have an answer but don't want to submit it in case I am totally off. Anyone mind double checking this for me to make sure I'm not way off base?I think the answer is the following: Z = 2 X = 4 y = 3Am I way off base...

Homework Statement Prove that is ##A## is lower triangular and ##B_{ij}## is the matrix that results when the ith row and jth column of A are deleted, then ##B_{ij}## is lower triangular if i > j. Homework EquationsThe Attempt at a Solution I know that a square matrix is lower triangular if...

This seems easy but when I tried to do this, the best way I came up with is to list all entries and then do the multiplication work. Is there any better ,clearer and more simple way to do the proof?

They look a lot like matrices, and seem to work exactly like matrices. What is the difference between them? I have only worked with matrices, not tensors because I can't find a tutorial online but every time I have seen one they seem identical.

Hi all, there is a facial detection program called eigenfaces that supposedly uses eigenvectors to recognise faces, can anyone here share any intuition on how that works or send a link? Any help apreciated.

sorry. erm.. what does the determinant means or functions in matrices , math? thanks..

Hi Everyone. Just a brief hello before the problem! I am a new user as of today. I am studying Electrical Engineering in my spare time after work, and currently working full time an electronics service engineer. I have tried to make the problem as clear as I can, any help would be highly...

Hello all, I have 3 matrices, A - symmetric, B - anti symmetric, and P - any matrix All matrices are of order nXn and are not the 0 matrix I need to tell if the following matrices are symmetric or anti symmetric: 1) 5AB-5BA 2) 4B^3 3) A(P^t)(A^t) 4) (A+B)^2 5) BAB How would you approach...

Homework Statement Given the ellipse ##0.084x^2 − 0.079xy + 0.107y^2 = 1 ## Find the semi-major and semi-minor axes of this ellipse, and a unit vector in the direction of each axis. I have calculated the semi-major and minor axes, I am just stuck on the final part. Homework Equations this...

I've attached the question to this post. The answer is false but why is it not considered the orthogonal projection? ## A = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix} ## ## B = \begin{bmatrix} x \\ y \end{bmatrix} ## ## AB =...

I'm trying to understand what makes a valid covariance matrix valid. Wikipedia tells me all covariance matrices are positive semidefinite (and, in fact, they're positive definite unless one signal is an exact linear combination of others). I don't have a very good idea of what this means in...

Hello, I am currently trying to study the mathematics of quantum mechanics. Today I cam across the theorem that says that a Hermitian matrix of dimensionality ##n## will always have ##n## independent eigenvectors/eigenvalues. And my goal is to prove this. I haven't taken any linear algebra...

Two questions, both about adjacency matrices (graphs). The first, specific, the second, general. [1] I read: "Consider a directed graph and a positive integer k. Then the number of directed walks from node i to node j of length k is the entry on row i and column j of the matrix Ak..." [where A...

OK so i can prove that the given inverse is actually the inverse but i can not prove that I+A is non singular without using the given inverse so how do i go about doing that?(I have done part a) Thanks in advance.

Find all values of h and k such that the system has no solutions, a unique solution, infinitely many solutions hx +6y =2 x (h+1)y =2k I can't seem to augment the matrix. Am I allowed to multiply buy variables h / k? I can find the determinant: h^2 +h -6 Then make it equal to 0 and solve; h =...

HI, I've been running through my lectures notes and have stumbled upon something i can't quite figure out. I am given Ψ(x)=∑a_iΨ_i(x) Then OΨ(x)=∑ a_i O Ψ_i(x) , where O is an operator acting upon Ψ Then i am given something which i don't quite understand, OΨ_i(x) = ∑ O_ji Ψ_j(x) , Where...

Homework Statement Generate a triangle. For this problem, generate a triangle at a grid of points that are finely spaced in the x dimension. The triangle is defined as follows: -Side 1: y = 0 for x = 0 to 2 -Side 2: x = 0 for y = 0 to 1 -Hypotenuse: y = 1-0.5x for x = 0 to 2 Alternatively, the...

Mod note: Moved from a technical section, so is missing the homework template. I am using matrix methods to do ray optics but my knowledge on matrices is behind. I found the system matrix to be \begin{bmatrix} \frac{-f_2}{f_1} & f_1 + f_2 \\ 0 & \frac{-f_1}{f_2} \end{bmatrix} I want to find...

Homework Statement The problem states that we have L as the linear transformation as: \begin{align*} A= \left( \begin{array}{ccc} 2 & 0 & 1 \\ -2 & 3 & 2 \\ 4 & 1 & 5 \end{array} \right) \end{align*} And when given another linear transformation T as: \begin{align*} B= \left( \begin{array}{ccc}...

I know that the matrices {\Gamma^{A}} obey the trace orthogonality relation Tr(\Gamma^{A}\Gamma_{B})=2^{m}\delta^{A}_{B} In order to show that a matrix M can be expanded in the basis \Gamma^{A} in the following way M=\sum_{A}m_{A}\Gamma^{A} m_{A}=\frac{1}{2^{m}}Tr(M\Gamma_{A}) is it enough to...