Re: About Linear Algebra

On 28.09.2006 18:27, Arturo Magidin wrote:

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).

.... maybe a 2x2-matrix A with characteristic polynomial x^2+1 would do?
.

Relevant Pages

  • Re: About Linear Algebra
    ... P/S: I denote transpose A as A^T ... 1)If AA^T is singular, then so is A; ... Arturo Magidin ...
    (sci.math)
  • Re: About Linear Algebra
    ... A is a square matrix ... P/S: I denote transpose A as A^T ... 1)If AA^T is singular, then so is A; ...
    (sci.math)
  • Re: About Linear Algebra
    ... and what is the reason: ... P/S: I denote transpose A as A^T ... 1)If AA^T is singular, then so is A; ...
    (sci.math)
  • About Linear Algebra
    ... and what is the reason: ... A is a square matrix ... P/S: I denote transpose A as A^T ...
    (sci.math)