Re: About Linear Algebra
- From: hrubin@xxxxxxxxxxxxxxxxxxxx (Herman Rubin)
- Date: 28 Sep 2006 13:58:16 -0400
In article <efgt56$2fet$1@xxxxxxxxxxxxxxxxxx>,
Arturo Magidin <magidin@xxxxxxxxxxxxxxxxx> wrote:
In article <1159460588.976226.114280@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
jack1234 <jackscience@xxxxxxxxx> wrote:
I would like to know the statement is always true or sometimes false,
and what is the reason:
Yeah; lost of people would like someone else to do their homework for
them.
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.
(2) is sometimes false, because there are examples of A^2 symmetric
but A not symmetric. (Probably not enough of a reason to satisfy
your teacher; oh, well; maybe you'll try to figure out an example
on your own).
(1) is true. Think determinants.
Don't work so hard. If AA^T is singular, there
is a non-zero vector v so that v^TAA^t = 0. Then
v^TAA^Tv = 0. But this is just (v^TA)(A^Tv), or
the sum of the squares of the elements of v^TA.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.
- References:
- About Linear Algebra
- From: jack1234
- Re: About Linear Algebra
- From: Arturo Magidin
- About Linear Algebra
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