Description:
Mathematical discussions and pursuits.
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? orth proj of rectangular matrix A
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Hi: If A is a square matrix, then the projector onto the range of A is given by P = A*inv(A*A')*A'. Its orthogonal complement, the null of its adjoint, is simply I-P, where I is an identity matrix of size N, which is the size of A. My question now is: what if A is an M-by-N rectangular matrix? How do... more »
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reconstructing a 2D bitmap
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Let's say I have a 2D grayscale bitmap, 640 pixels wide by 480 pixels tall. Let's also say that each pixel can have a value between 0 and 255, inclusive. Let's also say the bitmap is non-trivial: for example, not completely black or completely white. Can one derive two 1-D functions, which, when multiplied together,... more »
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Mann iterates
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If f : [0,1] --> [0,1] is continous, then the sequence defined by x_(n) = ( f(x_1) + ... + f(x_n) ) / n (x_1 in [0,1]) is convergent (to a fixed point of f). Does someone know a (simple) proof for this? Or a reference. Thank you, Mate
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"q-serie" Fourier transform
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Hi, I'm looking for Fourier transform (for -1<q<1) of a "q-serie" défined by: f(q,n)=(q;q)_n=product(1-q^m,m =1..n) (maple notations) So, a the first time, I calculate derivative of f(q,n) with the hope to simplify Fourier transform calculus. I have d_f(q,n)/dq=sum(d(1-q^m)/dq*pr oduct(1-q^k,k=1..n et k<>m),m=1..n)... more »
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Discrete math with not Euler...
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Hello teacher~ [link] Start from A. A scavernger's cart sweep along the street(edge). A scavernger's cart sweep all streets. Back to A. Find the shortest distance. ------------------------------ --------------------- This is not a Euler circuit. Anyway...think.... more »
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