Symmetric matrix Definition and 63 Threads

Homework Statement Prove a symmetric (2x2) matrix always has real eigenvalues. The problem shows the matrix as {(a,b),(b,d)}. Homework Equations The problem says to use the quadratic formula. The Attempt at a Solution From the determinant I get (a-l)(d-l) - b^2 = 0 which...

Guys does anyone know of a technique to find the exponential of a tridiagonal symmetric matrix... Thanks in advance

Homework Statement Let {u1, u2,...,un} be an orthonormal basis for Rn and let A be a linear combination of the rank 1 matrices u1u1T, u2u2T,...,ununT. If A = c1u1u1T + c2u2u2T + ... + cnununT show that A is a symmetric matrix with eigenvalues c1, c2,..., cn and that ui is an eigenvector...

Homework Statement consider the 2*2 symmetric matrix A = (a b ) (b c) and define f: R^2--R by f(x)=X*AX . show that \nablaf(x)=2AX Homework Equations The Attempt at a Solution quiet confuse about this question \nablaf(x)=(Homework Statement consider the 2*2 symmetric matrix A...

Homework Statement http://img266.imageshack.us/img266/152/78148531ur5.png Homework Equations A is symmetric. The Attempt at a Solution First of all if you calculate rT you'll get qTA so why it the order reversed in the picture above? Moreover I don't see why it is zero.

My question is; Let S = {A € Mn,n | A = AT } the set of all symmetric n × n matrices Show that S is a subspace of the vector space Mn,n I do not know how to start to this if you can give me a clue for starting, I appreciate.

Hi there, I would appreciate if you could share your exeriences or ideas about properties of 4x4 symmetric/hermitean matrices H such that U^T H U = D = diag( E1, -E1, E2, -E2 ) or diag (E1, E2, -E1, -E2 ) The things I would like to perform are the following - decompose an expression...

Homework Statement Hi, I need to prove that if S is a skew-symmetric matrix with NXN dimension and B is any square real-valued matrix, therefore the product of transpose(B), S, and B is also askew symmetric matrix Homework Equations This is what I know so far. 1.Transpose(S) = -S...

Let A in n x n real matrix. For every x in R^n we have <Ax,x>=0 where < , > is scalar product. prove that A^t=-A (A is skew symmetric matrix)

This is a T/F question: all symmetric matrices are diagonalizable. I want to say no, but I do not know how exactly to show that... all I know is that to be diagonalizable, matrix should have enough eigenvectors, but does multiplicity of eigenvalues matter, i.e. can I say that if eignvalue...

I would like to know the statement is always true or sometimes false, and what is the reason: A is a square matrix P/S: I denote transpose A as A^T 1)If AA^T is singular, then so is A; 2)If A^2 is symmetric, then so is A.

Hello all. I'm stuck with this excercise that is asking me to proof that the determinant of the nxn matrix with a's on the diagonal and everywhere else 1's equals to: |A| = (a + n - 1).(a-1)^(n-1) So the matrix should look something like: [a 1 1.. 1] [1 a 1.. 1] [: ... :] [1 ..1 1...

Hello everyone! Can anyone help me here in this theorems (prove)? (Or solve) 1. Suppose that A and B are square matrices and AB = 0. (as in zero matrix) If B is nonsingular, find A. 2. Show that if A is nonsingular symmetric matrix, then A^-1 is symmetric. I hope these won't...