November 2012
Intermediate to advanced
794 pages
22h 9m
English
book
Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
by John J. Shynk
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G.1 BASIC PROPERTIES
Consider matrix 
with N columns {an} and M rows 
as follows:
(G.1) 
where the superscript T denotes matrix/vector transpose. The scalar elements of A are denoted by {amn}. All vectors in this book are defined to be column vectors; row vectors are obtained by using T.
Definition: Linearly Dependent The columns of A are linearly dependent if there exist nonzero {xn} such that
(G.2) 
where 
and 
is a column vector of zeros. Otherwise, they are linearly independent.
A similar definition applies to the rows of A.
Definition: Rank The rank r of matrix A is the number of linearly independent columns, which is also the number of linearly independent rows.
Obviously 
. Assume for the next set of definitions that is a square matrix with M = N.
Definition: Symmetric Matrix A is ...
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.