so, the union of a basis of with a basis of is a basis of .
I can see that this is true but I am having trouble presenting a convincing argument.
Let V = . Show that V has a basis with the property that each matrix in the basis is either symmetric or skew symmetric.
The second part of the question however I have no idea where to start:
Show also that V has a basis with the property that each matrix in the basis is an invertible matrix.