00:01
Since we know a is orthogonally diagonalizable, we can write a as a equals p -d -p inverse, where p is an orthogonal matrix and d is a diagonal matrix.
00:18
And we also know that a is invertible, so we can take the inverse of both sides of the equation.
00:25
So now we have a -inverse equals the inverse of p -d -p -inverse.
00:34
And using the property of inverse, we're basically distributing the inverse into the expression between the parentheses and reverse the expression.
00:49
So now we have the inverse of p inverse times d inverse times p inverse.
01:02
And now the inverse of p inverse is just p itself.
01:07
So now we have the expression like this.
01:15
Also we know that d is a diagonal matrix.
01:20
So the inverse of a diagonal matrix is still a diagram matrix.
01:27
We can call it b...