| [ |
| { |
| "text": "Why is that first statement true?" |
| }, |
| { |
| "text": "Huh." |
| }, |
| { |
| "text": "Huh." |
| }, |
| { |
| "text": "How is that matrix related to this matrix?" |
| }, |
| { |
| "text": "It's just a transpose." |
| }, |
| { |
| "text": "If I take the transpose of that matrix, I get that." |
| }, |
| { |
| "text": "So what happens to the trace?" |
| }, |
| { |
| "text": "I'm adding down the diagonal." |
| }, |
| { |
| "text": "The transpose has no effect." |
| }, |
| { |
| "text": "Clearly, this is just the fact that the trace doesn't change, is not changed when you transpose a matrix, because the diagonal is not changed." |
| }, |
| { |
| "text": "Now, what about this guy?" |
| }, |
| { |
| "text": "I guess we're getting back to old fashioned 18.065, remembering facts about linear algebra, because this is pure linear algebra." |
| }, |
| { |
| "text": "So what's this one about?" |
| }, |
| { |
| "text": "This says that I can reverse the order of two matrices." |
| }, |
| { |
| "text": "I'm now looking at the connection between those two." |
| }, |
| { |
| "text": "And so let me just use different letters." |
| }, |
| { |
| "text": "CD equals the trace of DC." |
| }, |
| { |
| "text": "I can flip the order." |
| }, |
| { |
| "text": "That's all I've done here is I've reversed B with A transpose." |
| }, |
| { |
| "text": "I reversed C with D. OK, so why is that true?" |
| } |
| ] |
