Transpose Definition and 92 Threads

Homework Statement Orthogonal matrix means Q^{T}Q=I, but not necessary QQ^{T}=I, so why can we say the inverse of Q is Q^{T}? Homework Equations The Attempt at a Solution the attempt is actually in my question. It's something i don't understand when doing revision.

Homework Statement Find a formula for (ABx)T, where x is a vector and A and B are matrices of appropriate sizes. Homework Equations (AB)T = BTAT among a few others, probably the most relevant one with transposes here. The Attempt at a Solution I'm wondering what this "formula"...

I have a real nxn matrix A and I want to find P, so that P-1AP=AT. Does such a matrix exist? How do I find it? What if I have two matrices A,B. Does there exist a matrix P, that transforms both of them to their transposes? Thanks

I'm sure there are a ton of ways to interpret what the transpose of a matrix represents. Could someone just give me a laundry list of interpretations? Thanks!

What is the geometric interpretation of the transpose of a matrix? Is there any physical significance of the matrix transpose?

If the transpose of A equals the Inverse of A, then det(A)=1. False. However, I don't follow the logic. If transA=InverseA, doesn't that mean the matrix is the identity matrix? The explanation says that det(A)= 1 and -1.

A transpose of a nonsingular matrix is nonsingular. This is true; however, how can this be done without using determinants? I know how to do this with determinants so please don't inform how to do this with determinants.

Homework Statement Prove all eigenvalues = 1 or -1 when A is circulant and satisfying A=A^T=A^-1 I can think of an example, the identity matrix, but i can't think of a general case or how to set up a general case. Homework Equations The Attempt at a Solution I can only show by...

Homework Statement Hi guys If I have a vector v, then is it correct notation to write \mathbf v = \left( {\begin{array}{*{20}c} {v_1 } \\ {v_2 } \\ \end{array}} \right) = (v_1,v_2)^T, where T is the transpose?

Homework Statement Prove or disprove: A and AT have the same eigenspaces. Homework Equations The Attempt at a Solution I know that A and AT have the same determinant and so they have the same characteristic polynomial and eigenvalues, but then if they are transposed then the...

I would like to demonstrate an identity with the [SIZE="4"]INDICIAL NOTATION. I have attached my attempt. Please let me know where I made mistakes. Any suggestion? I am trying to understand tensors all by myself because they are the keys in continuum mechanics Thanks

Homework Statement I have an idea on how to part 1, but I have no clue on how to do part 2 and 3. 1.Suppose A is invertible. Check that (A-1)TAT=I and AT(A-1)T=I, and deduce that AT is likewise invertible with inverse (A-1)T. 2. Suppose A is an mxn matrix with rank 1. Prove that there...

In particle physics, we commonly have the gamma matrices, whose conjugate transpose is the raised or lowered index. Does the same rule apply to ANY indexed quantity? What about to scalar/vectors like momentum. Is the conjugate of momentum: \left(q_\mu\right)^\dagger = q^\mu The...

Hey guys, So I've actually learned a fair bit about trig identities the last few weeks and beginning to understand how they actually work thanks to Irrational, Mute and some prompting from Hurkyl. I'm still having trouble with transposing which I think should be fairly simple. The equation...

Hi Guys, Simple question; I'm trying to work out the transpose of Y = Sin(x) + Cos(x) to make x the subject. I thought it would be x = arccos(arcsin(y)) / 2 however I don't think that's right. Is there another theorem I'm missing?

Homework Statement I don't understand why the determinant of a matrix is equal to its transpose...how is this possible? Homework Equations The Attempt at a Solution

I have a bunch of row vectors saved as objects r1 r2 r3. I would like to send each set of data (row) to a text file, but I want it to save as a column. This means that I want to save the transpose of the data, i.e., r1' r2'... Unfortunately, when I try to use save r1.txt r1' -ascii MATLAB...

Hi! I'm working on a programming project(fortran 77). and I need to transpose a big matrix, and for the moment I'm doing it by to do-loops: DO 20 J = 2,NP DO 10 I = 1,J-1 T = P(I,J) P(I,J) = P(J,I) P(J,I) = T 10 CONTINUE 20...

Eigenvalue and eigenvector for a symmetric matrix Homework Statement Let A be a n by n real matrix with the property that the transpose of A equals A. Show that if Ax = lambda x, for some non-zero vector x in C(n) then lambda is real, and the real part of x is an eigenvector of A...

I have been battling with this for hours now, i just keep getting stuck. It is to show that: (xyT)+=(xTx)+(yTy)+yxT After expanding the left side, leting xyT=A. I get stuck at (yxTxyT)+yxT I have tried from both sides of the equation, but can't arrive at the expected result. Any clues?

Hi Could somebody please tell me what the use is for the transpose of a matrix, and maybe give an example if possible. Thanks

Every book I've seen starts out with "to find the transpose, make B_ij = A_ji . However, they don't explain exactly why would would want to do this. Ie. they tell you the inverse is useful because if you have Ax = b, you can find x by writing b = A^{-1} x. The only thing I can think of to...

Say, \psi^1,\ \psi^2 are Dirac spinors, and M is a matrix composed of Dirac matrices. Is the following equation hold? \bar{\psi^1}M\psi^2 = -\Big(\bar{\psi^1}M\psi^2\Big)^T I'm not quite sure, here is my derivation: \bar{\psi^1}M\psi^2 = \bar{\psi^1}_{i}M_{ij}\psi^2_j = -...

Hi, I'm currently trying to decipher an equation in a paper I'm reading for research of my own. However, I am running to a little trouble interpreting their notation and was hoping some of the knowledgeable people on this forum might be able to help. I have attached the image containing the...

B= A transpose What is the relation between ker(BA) and ker(A)? I was told that they are equal to each other, but I can't figure out why. ker(A) => Ax = 0 ker(BA) => BAx = 0 so that BA is a subset of A. This shows that ker(BA) =0 whenever ker(A) = 0, but how does this also show that...

Homework Statement Show that if an nxn matrix A has n linearly independent eigenvectors, then so does A^T The Attempt at a Solution Well, I understand the following: (1) A is diagonalizable. (2) A = PDP^-1, where P has columns of the independent eigenvectors (3) A is...

if you want to find the derivative (gradient) of f(x)^2 when f is a vector, you would get 2*f(x)*del(f(x)) I never know where to put the transpose! sometimes its clear because another term in the equation will be a scalar, so you know an inner product is needed, but if you don't have a...

So I've shown that A and A^T have the same char. polynomials => same eigenvalues, using the fact that detA = detA^T. I still can't see any way I could possibly show or disprove that the eigenspace is the same.

I need help on the tranpose of a multiple of a matrix. I need to prove: transpose(AB)=transpose(B)*tranpose(A) Any Ideas?

Let A be a nxn matrix. Prove that if (A*)A=0 then A=0. What if A(A*) = 0? A* is the conjugate transpose of A. When I write out the expansion formula, I cannot conclude that every entry of A is zero. What am I missing?

if i have a matrix A, and i want to find it's transpose on MATLAB i.e. i want to find A^T but how do i do that on matlab...what command do i type in?

Is the adjoint of linear map only guaranteed to be equivalent to the conjugate transpose of the matrix when the matrix is taken with respect to an orthonormal basis? Is it sometimes still equivalent even when the basis is not orthonormal? For the problem I'm working on, I have...

The question that I am stuck on is: Show that if X" (double dual of X) is identified with X and U" (double dual of U) with U via the duality relation, then T" (double transpose) = T. (Duality relation is f(L) = L (x) where f is in X", L is in X', and x is in X) So far, here is my work...

I haven't written a proof in 8 years. Linear Algebra proofs are going to be the death of me. I honestly don't know where to begin. I read a sort of primer on proof writing, but I could use a human walk through or some help. So far, I have: there exists a B such that AB = BA = I...

(ABC)^T, A,B,C are all symmetric, then why isn't (ABC)^T = CBA? If you consider that (ABC)^T = (C^T)(B^T)(A^T) and in symmetrix cases, then C^T = C and so on...? (Latex edit by HallsofIvy)

Hi, I'm having trouble with a proof regarding the rank of the transpose of a matrix. Here's the question: Let A be an m x n matrix of rank r, which is of course less than or equal to min{m,n}. Prove that (A^t)A has the same rank as A. Where A^t = the transpose of A. I can easily...

how do you prove: (AB)^T=C^T=B^T*A^T?

hmmm...I have problems understanding this...how can the null space if a matrix(not necessarily a square) be the same as that of its transpose? Thanks in advance

What are the relations between a matrix H and its transpose H^T? I am not asking about the relations between the coefficients, I am asking the relations as linear maps (H: F^m->F^n; H^T: F^n->F^m). I am not sure exactly how I should pose the question actually, but I am thinking there is some...

I'm not sure if I am making a mistake, or my book is wrong, or if both answers are correct. But, it is confusing me, and I would like to know why. We are asked to find the basis of the following subspaces on the matrix A. Find: R(A^T),\,\,N(A),\,\,\,R(A),\,\,N(A^T) I'm having trouble...

I am interested in a system of natural units that I see used more and more frequently in Quantum Gravity research papers so I like to try using them. the units are like conventional Planck except |8piG| = 1 I want to see if there is anything in the Cambridge Handbook of Physics Formulas...

I've been doing revisions for my final exams, and I got stuck on the proof det A = det A^T, determinant of A = determinant of A transpose. How do I proof it?