U1L3j.txt

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So unitary one o columns unit orthogonal.
Two, all rows are units, and vectors and orthogonal vectors.
Three, takes com-- takes units vectors to unit vectors.

And four, u is equal to u dagger point.
No, u inverse is equal to u dagger.

So I should tell you some notation if you don't know it.
m dagger is equal to m conjugate transpose.

So I will prove one direction of this.
I'm not going to bother proving the other.
If you have the textbook, it's in the textbook.
So if u is equal to c1, c2 through c17 minus 1,
u adjoint--
this is called adjoint--
is equal to c1 star, c2 star through c d minus 1 star.

And now, suppose we take u dagger u.
We are multiplying the i's column
of u sub dagger with the--
or rather, we're multiplying the row of u dagger
with the j's column of u.
So this is equal to c1 dagger, c1, c1 dag--
c1 transconjugate c2 through c2 conjugate, c2, et
cetera, which equals 1, 1, 1, 1, 1, 1.
Because cj dagger, ci is zero unless i
equals j, in which case it's 1.
So that says that u conjugate transpose
is the inverse of u, which is condition number four.