- #1
robierob12
- 48
- 0
Lately I have been been studying basis and demension.
For a more interesting problem I wanted to see if I could find the basis of the vector space of all 3x3 skew symetric matricies.
Usually, I can find a general form for these types of problem. Such as the general form of a symetric matricie. But skew symetric matricies seem to have more than one form
[0 a b]
[-a 0 c]
[-b -c 0]
and
[0 a -b]
[-a 0 -c]
[b c 0]
I proved that this form of a skew symetric matrice is a basis
[0 a b]
[-a 0 c]
[-b -c 0]
but is it true for the vector space of all 3x3 skew symetric matricies of that form or all skew symetric matricies?
For a more interesting problem I wanted to see if I could find the basis of the vector space of all 3x3 skew symetric matricies.
Usually, I can find a general form for these types of problem. Such as the general form of a symetric matricie. But skew symetric matricies seem to have more than one form
[0 a b]
[-a 0 c]
[-b -c 0]
and
[0 a -b]
[-a 0 -c]
[b c 0]
I proved that this form of a skew symetric matrice is a basis
[0 a b]
[-a 0 c]
[-b -c 0]
but is it true for the vector space of all 3x3 skew symetric matricies of that form or all skew symetric matricies?