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Prove that $\langle X,Y\rangle:= \mathbb{E}[XY] $ makes $\mathcal{H}$ into a real inner product space

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#analysis #solution-verification #hilbert-spaces #expected-value #inner-products
75
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Make two matrices perpendicular by orthogonal transformation

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#linear-algebra #inner-products #orthogonal-matrices
74
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Is the following operator a positive operator?

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#linear-algebra #functional-analysis #hilbert-spaces #inner-products #tensor-products
250
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Looking for an alternative and easier way to prove Sylvester's theorem

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#linear-algebra #matrices #inner-products #symmetric-matrices
78
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Does positive correlation of vectors depend on the inner product?

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#linear-algebra #examples-counterexamples #inner-products #positive-definite #positive-semidefinite
124
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Is the cosine angle between two R.V. an (approximation) not equality to the correlation coefficient?

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#statistics #inner-products #variance #covariance #correlation
50
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What is the value of $\left< e^{-|x|}\left| \left(i\frac{d} {dx}\right)^2 \right|e^{-|x|}\right> $?

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#expected-value #inner-products #positive-definite
338
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Isometry preserves dot product?

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#abstract-algebra #inner-products #isometry
46
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Use Gram-Schmidt to find an orthonormal basis of a product of two polynomials.

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#linear-algebra #inner-products #orthonormal #gram-schmidt
251
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Dot Product Cone

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#vector-spaces #vectors #inner-products
77
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Solving inner product equation

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#linear-algebra #normed-spaces #inner-products
83
Views

Reverse differential on Riemannian manifolds

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#category-theory #riemannian-geometry #inner-products
43
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Reference Request: Numerical Integration of Interpolation Formulas

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#numerical-methods #inner-products #interpolation #quadrature #discrete-calculus
200
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well-defined inner product

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#functional-analysis #inner-products #c-star-algebras
107
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Cauchy Schwarz Inequality for Vectors - Quadratic form Clarification

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#vectors #inner-products #quadratic-forms #cauchy-schwarz-inequality #discriminant

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