Find a basis for the space of 2x2 symmetric matrices

  • #1
a)Find a basis for the space of 2x2 symmetric matrices. Prove that your answer is indeed a basis.
b)Find the dimension of the space of n x n symmetric matrices. Justify your answer.
 

Answers and Replies

  • #2
10
0
The space of 2x2 matrices is in general isomorphic to a very familiar space. Think about the way addition of matrices and scalar multiplication work, and you should figure this out (and if you think about this for a while, you might realize a more general property about finite vector spaces over a field). From there, you should realize that the symmetric matrices are a subspace. If you look at some examples of 2x2 symmetric matrices, you should see the pattern.
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,847
966
A general 2 by 2 symmetric matrix is of the form
[tex]\begin{bmatrix}a & b \\ b & c \end{bmatrix}[/tex]
you should be able to get a basis and the dimension from that.
 

Related Threads on Find a basis for the space of 2x2 symmetric matrices

Replies
3
Views
6K
Replies
1
Views
28K
Replies
2
Views
4K
Replies
5
Views
13K
  • Last Post
Replies
7
Views
5K
Replies
6
Views
3K
Replies
6
Views
31K
Replies
1
Views
2K
  • Last Post
Replies
6
Views
2K
Replies
2
Views
4K
Top