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