------5.2
Direct Sums
Block matrices
Talk about block matrices
Start with the 1x1 block matrices
Do bigger blocks
Do block multiplication
Direct sums equivalent definitions
The following are equivalent:
direct sum
sums and unique way of writing 0
unique way of writing any element
union of ordered basis for summands is ordered basis
exists order basis fof summands so that union is ordered basis.
See book for proof
Diagonalizabla if and only if there is a decomposition of V into eigenspaces.
5.3
Machov