Recent content by NaturePaper

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    Graduate Does AA^\dagger=I Imply A^\dagger is the Generalized Inverse of A?

    No. In my question A\dagger was conjugate transpose and conditions 3 and 4 in Penrose's definition are just the requirement that AX and XA both should be hermitian, where X is the generalized inverse of A (in my case which is A\dagger and so 3-4 follows trivially).
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    Graduate Does AA^\dagger=I Imply A^\dagger is the Generalized Inverse of A?

    It looks the answer is yes. The result can be found in http://en.wikipedia.org/wiki/Proofs_involving_the_Moore%E2%80%93Penrose_pseudoinverse" .
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    Graduate Does AA^\dagger=I Imply A^\dagger is the Generalized Inverse of A?

    Hi, Does the equation AA^\dagger=I force A^\dagger to be the generalized inverse of A? That is: AA^\dagger=I\Rightarrow A^\dagger\text{ is the generalized inverse of } A? A is any rectangular matrix over the field of complex numbers. It is very easy to verify the first three properties, but...
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    Undergrad Does there exists a matrix who's product is itself?

    Hello mscudder3, Take any unit column vector a (i.e., nx1 matrix with sum of square of moduli of its elements being 1, where n is the number of your choice). Then the matrix m=aa^\dagger will satisfy m^2=m.
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    Graduate Silly question about matrices with matrix elements

    Well, I thought (and still think) Landau is a specialist in Quantum Mechanics (which is sometimes called the mathematical modelling of nature and uses lots of linear operators:P). Particularly, the whole matrix theory is a basic tool in finite dimensional QM and its modern branch Quantum...
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    Graduate Silly question about matrices with matrix elements

    @Landau, Hey, I hope u know how to erase it :D
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    Undergrad Differentiability and Continuity

    Well said...Really I am feeling jealous to you for such a nice answer! Regards, NP
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    Graduate Non-zero eigenvalues and square matrix

    Yes, your explanation is correct too. By the way, these are very much elementary results and there is no confusion that these can be found in all textbooks of matrix theory/linear algebra :)
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    Graduate Non-zero eigenvalues and square matrix

    I think you have missed the word in red :) Ya, both 1 and 2 are correct. However what you ask in the last part, I don't understand it..
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    Graduate Do these curious identities hold true?

    Then what is x_k (I don't think it is a finite number) and then what is meant by your last derivation? :)
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    Graduate Measure of Irrationals with Even First Digit

    Surely I am missing some simple points, but what about say [.11, .12]? Every real within this interval must start with 1 and so does not contain any such number?
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    Graduate Show that for a symmetric or normal matrix

    If you are trying some short cuts (:)), what wrong with considering Spectral form of http://en.wikipedia.org/wiki/Spectral_theorem#Normal_matrices"?
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    Graduate Show that for a symmetric or normal matrix

    I don't know what is the function of JCF in it...it simply follows from the well known Caley-Hamilton Theorem (Every square matrix satisfies its own characteristic equation) and the result holds for any square matrix.
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    Graduate Maximum of a trigonometric function

    Oh, finally I got an answer to this question...the proof is a handy one (according to me, of course!:smile:). The answer is indeed correct. Since \cos\theta_1\cos\theta_2\sin\theta_1\sin\theta_2\ne0, \cos\theta_1,\cos\theta_2,\sin\theta_1,\sin\theta_2<1. so...
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    Graduate Maximum of a trigonometric function

    Plotting in mathematica with different values, I can not find an exception. But the reasoning of closed, compact domain can not be applied, because though the domain is convex, the function is itself not a convex one. However, we can split the domain such that in each part, the function...