Recent content by tom08

can someone give me a hand?

can someone give me a hand?

if || x - A y|| = || (x - y) + (y - Ay) ||, then || x - A y|| <= || (x - y) || + || (y - Ay) ||, but how could u find that C = sup |x-Ax| for all x ? notice that my esitmate is C*||x-y||

no, please look at my wiki link in the last secion, "rectangular matrix" if Q is not square, but column orthonormal. let Q be an n-by-m matrix, and (m<n), then Q'*Q=I, but Q*Q'<>I. so i want to find out an upper bound of ||I-Q*Q'|| w.r.t m, where m is the number of orthonormal columns...

Homework Statement If A is a rectangular n*m matrix (n>m) , and all the columns of A is orthonormal. I know that A'*A=I, where A' stands for its transpose. but A*A'<>I as I've learned from wiki. but is there an estimate for \|A \cdot A'\| ? Homework Equations...

Could u show me any hints about ur estimate for C. I only figure out that \|x-Ay\|=\|(x-Ax)+(Ax-Ay)\|\leq\|I-A\| \|x\|+\|A\| \|x-y\| I don't know how to continue... could anyone kindly give me more hints ?

Thank you for ur kind help. if all the entries of A is between 0 and 1, can we get a nicer upper bound ?

Homework Statement assume that x and y are vectors, and A is a matrix. can anyone kindly help me to find an upper bound C w.r.t \| A \| s.t. \| x-Ay \| \leq C \cdot \| x-y\|

Thank u, vela and rock. i realize my mistake.

thank u so much. BTW, is there an upper bound for |A'*A-A*A'| when A is a rectangluar column orthogonal matrix?

Thanks for ur kind reply. but must A and B be square such that the following equation holds ? (A'B)'=B'*A I think that if A*A'=I (wheter is square or not), we take transpose operator on both sides of the equation, and obtain that (A*A')' = I' then A*A' = I

Homework Statement I encounter a strange problem. Let A= [1.0000 0 0 0 0 0 0 0 0.4472 0 0.3162 0 0 0.9487 0 0 0 0.8944] I am surprise to find that A'*A=I...

Homework Statement Hi, everyone! I encounter a problem as follows: I have got a matrix A, all the entries in A is between 0 and 1. and the sum of each row of A is 1. Can we say that all the entries in Ak is also between 0 and 1 ? Can everyone kindly show me how to prove it when...

Homework Statement Given a real diagonal matrix D, and a real symmetric matrix A, Homework Equations Let C=D*A. The Attempt at a Solution How to prove all the eigenvalues of matrix C are real numbers?

Help! Symmetric matrix I know that all the eigenvalues of a real symmetric matrix are real numbers. Now can anyone help out how to prove that "all the eigenvalues of a row-normalized real symmetric matrix are real numbers"? Thank you~~~