- #1
chefobg57
- 8
- 0
Hi!
I am working on the following problem:
If a matrix is antisymmetric (thus A^T = -A), show that
P = {A [tex]\in[/tex] R | A is antisymmetric} is a subset of Rnxn. Also, find the dimension of P.
So far, I've proven that P is a subset of R and I am guessing that, in order for me to find the dimension, I need to find the basis of P first. Here is where I am kind of stuck.
I understand what the properties of the base would be (1. the vectors inside the set will be linearly independent and 2. the basis will be a spanning set for P), but how exactly should I start working so that I can find the basis itself...
A hint would be highly appreciated!
Thanks a bunch guys!
I am working on the following problem:
If a matrix is antisymmetric (thus A^T = -A), show that
P = {A [tex]\in[/tex] R | A is antisymmetric} is a subset of Rnxn. Also, find the dimension of P.
So far, I've proven that P is a subset of R and I am guessing that, in order for me to find the dimension, I need to find the basis of P first. Here is where I am kind of stuck.
I understand what the properties of the base would be (1. the vectors inside the set will be linearly independent and 2. the basis will be a spanning set for P), but how exactly should I start working so that I can find the basis itself...
A hint would be highly appreciated!
Thanks a bunch guys!