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accepted Gram matrix invertible iff set of vectors linearly independent
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revised logarithm of a matrix base a matrix — $\mathbf{A}^x = \mathbf{B}$
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answered Question about path-finding
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7
comment Choosing set of best estimators for linear least squares
You mention that your basis functions may even be repeated, but that this poses no problem for you since least-squares is well defined even in this case. Is that actually true? Are you also doing an $\ell_1$ or $\ell_2$ penalization on the weights?
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accepted What is $\text{cov}(Y,Y)$ given $\text{cov}(X,Y)$ and $\text{cov}(X,X)$
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accepted Using complex exponentials as solution of ODE
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5
asked What is $\text{cov}(Y,Y)$ given $\text{cov}(X,Y)$ and $\text{cov}(X,X)$
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asked Singular Distribution
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3
comment Gram matrix invertible iff set of vectors linearly independent
@Qiochu I know, by Gram-Schmidt, how to find the orthonormal basis that you mentioned. I can then represent each vector in my original set by this basis, thereby reducing the dimension of the vectors to equal the dimension of the subspace that they span. Do you think there is a way to demonstrate the property I'm asking about without requiring this reduction?
May
3
comment Gram matrix invertible iff set of vectors linearly independent
This only works if $A$ is square which assumes that there are as many vectors in the set as there are dimensions in each vector. Consider for example $v_1=<1,0,1>$ and $v_1=<0,1,1>$. Then $G=\begin{array}{cc} 2 & 1 \\ 1 & 2 \end{array}$, whose determinant is non-zero.
May
3
asked Gram matrix invertible iff set of vectors linearly independent
May
2
asked Arrow in limit operator