┌───┬───┐ ┌──────┬───────┐ ┌────────┬─────────┐
│ A │ B │ │ L0 │ 0 │ │ +⍉L0 │+⍉ T x L0│
├───┼───┤ = ├──────┼───────┤ x ├────────┼─────────┤
│+⍉B│ C │ │T x L0│ L1 │ │ 0 │ +⍉L1 │
└───┴───┘ └──────┴───────┘ └────────┴─────────┘
| ✔ |
(a) A |
= L0 x +⍉L0 |
| |
|
(b) B |
= L0 x +⍉ T x L0 |
| L0 x +⍉ T x L0 |
|
| L0 x +⍉ ((+⍉B) x ⌹A) x L0 |
definition of T |
| L0 x (+⍉L0) x (+⍉⌹A) x +⍉+⍉B |
+⍉ A x B ←→ (+⍉B) x +⍉A |
| L0 x (+⍉L0) x (+⍉⌹A) x B |
+⍉+⍉B ←→ B |
| A x (+⍉⌹A) x B |
(a) |
| A x (⌹A) x B |
A
and hence ⌹A are Hermitian |
| I x B |
associativity; matrix inverse |
| B |
identity matrix |
|