- #26

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My bad, I thought he just wanted a normal matrix.I‘m sure you missed a lot, say, a skew-Hermitian.

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- #26

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My bad, I thought he just wanted a normal matrix.I‘m sure you missed a lot, say, a skew-Hermitian.

- #27

Dick

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That is horrible beyond belief. You really don't listen to yourself talk, do you? Anybody that would believe that's a proof of anything, and I'm not even sure what you are trying to prove with that, would be a complete sucker. How many hundreds of posts have we had? You might recall I asked you to prove the entries of a diagonal matrix were 0 or 1. What's that garbage?Ok Let T^{8}v=w. Now if T^{9}=T^{8},

then T^{9}v=T^{8}v. Now we have T^{9}v

=TT^{8}v=Tw. Tw=w. Now if Tw=w, then TTw=Tw.

- #28

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by itself (no matter how many times) you'd get the same matrix. I just don't know how to prove it.

- #29

Dick

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If you don't know how to prove it, just say so. Don't post nonsense instead. WHY do you do that!! It's REALLY annoying. I would suggest you reread the whole thread, take a stress pill and think about it. Anybody else that want's to chip in here, take over. Actually, I'm the one who should take a stress pill.

by itself (no matter how many times) you'd get the same matrix. I just don't know how to prove it.

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- #30

Dick

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If the entries of a diagonal matrix are 1's and 0's would you know how to prove it?

by itself (no matter how many times) you'd get the same matrix. I just don't know how to prove it.

- #31

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I feel dumb. I mean this is such a simple concept...Take T and let it be diagonal. Now if T is diagonal and T^9=T^8, then T^9=/=T^8 if any of T's entries were >1 or <0.If the entries of a diagonal matrix are 1's and 0's would you know how to prove it?

Wait, are you implying that we know that T's entries are 0 's or 1's?

I mean if so: If T^9=T^8 , and we know that T's entries are either 0 or 1,

then T^n=T.

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- #32

Dick

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Never knew what a unitary transformation is, so I looked it up on wikipedia.

But yes x^9=x^8 equate when x=1 or 0. I was edging on that two posts ago by

saying that T^9=T^8 when their elements are not less than

0 or not greater than 1. But I guess it was on the shallow side. So about T=U*D*U^-1.

Does D* get multiplied by U* followed by U^-1 cancelling out the "effects" of U? If so, then

all we really knew from the beginning is that D is diagonal, obviously a diagonal matrix doesn't

need to have zeroes or ones on its diagonal.

- #34

Dick

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pretty much shown D^2=D. I was thinking that the proof was done already.

I was wrong.

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But I guess if T=UDU^(-1) and U is unitary, then T=D. So

T^2=(UDU^(-1))^2=D^2. If D^2=D, then T^2=T.

T^2=(UDU^(-1))^2=D^2. If D^2=D, then T^2=T.

- #37

Dick

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Oh so you mean U transforms D into a matrix that represents the basis where D came from, right?

Or is it that U transforms D into a matrix that represents T?

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- #39

Dick

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Both basically. U does one, U^(-1) does the other.

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