Register to reply

Lower bound on det(A'DA) with A tall and D diagonal?

by Wrukproek
Tags: bound, detada, diagonal, tall
Share this thread:
Jan20-13, 03:06 PM
P: 1
Hi all,

I searched all other threads but was unable to find something useful. Here is my question: I am looking for a lower bound on


where A is a MxN with M>=N (possibly tall and skiny) and D is diagonal, non-negative and of dimension M. In particular, I am looking for ways that separate the properties of the matrices A and D in this expression. I know that for M=N, we can rewrite it as

(1) det(A'*D*A) = det(A)^2*det(D),

which is very helpful. However, for the more general case with M>N, which is the one I am interested in, I am unable to derive a useful equality or lower bound (which would also be fine) that separates the matrices A and D in (1). Upper bounds are not useful in my particular application.

Thanks a lot for your help,
Phys.Org News Partner Science news on
New type of solar concentrator desn't block the view
Researchers demonstrate ultra low-field nuclear magnetic resonance using Earth's magnetic field
Asian inventions dominate energy storage systems

Register to reply

Related Discussions
Greatest lower bound/least upper bound in Q Calculus 1
Least upper bound/ greatest lower bound proof Calculus & Beyond Homework 4
Upper bound and lower bound Calculus & Beyond Homework 1
How do we find the least upper bound and greatest lower bound? Calculus & Beyond Homework 2
Upper bound/Lower Bound Set Theory, Logic, Probability, Statistics 10