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Dear R users, I want to know, given a curve f in d-dimensional space, It is possible to keep the curve’s shape and size unchanged by an arbitrary dxd orthnormal matrix A? That is, the new curve g = A*f is still the same shape and size as f? Thanks for your advices and answers. Fred [[alternative HTML version deleted]]

I believe eigen(), svd() and qr() can all do it. Andy > From: Jonathan Baron > > On 06/17/04 19:04, Fred wrote: > >Dear R-listers: > > > >I am trying to test an algorithm on a set of linearly > independent vectors > >{x1,x2,...,xn}. > > Well, here's an idea, for 10 vectors of length 10, > as columns of a matrix m1. The 11th seems to be needed.

Dear All Maybe the following is a stupid question. Assume I have 3 coordinate points (not limited to be in 2D or 3D space) a, b, c. It is known that these 3 points will define a plane. The problem is how to get the normal direction that is orthogonal to this plane. Is there an easy way to calculate it using the values of a, b, and c? Thanks for any point or help on this. Fred

Dear R users, I have a statistical question regarding on the Edgeworth expansion of a random vector. Assume x is a d-dimensional random vector, and whats the expression of its Edgeworth expansion up to order 4? I only get the formulation for a scalar random variable. So anyone can help me out on this problem? Thanks for your comments or advice. Fred [[alternative HTML version deleted]]

Dear R-listers: I am trying to test an algorithm on a set of linearly independent vectors {x1,x2,...,xn}. So anyone can give me a hint on generating these vectors in an easy way? Thanks for your points. Fred [[alternative HTML version deleted]]

Dear All Do you know some functions that can perform the PRINCIPAL SURFACE estimation? Please give me a hint. Thanks for your help in advance. Fred [[alternative HTML version deleted]]

Dear All, I want to know if there is some easy and reliable way to estimate the number of dominant eigenvalues when applying PCA on sample covariance matrix. Assume x-axis is the number of eigenvalues (1, 2, ....,n), and y-axis is the corresponding eigenvalues (a1,a2,..., an) arranged in desceding order. So this x-y plot will be a decreasing curve. Someone mentioned using the elbow (knee)