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Is dot product a kind of linear transformation

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#linear-algebra #linear-transformations #inner-products
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For $||x|| \leq ||y||$ is it true that $||x||^4 + ||y||^4 - 2\langle x, y \rangle ^2 \leq 3 ||y||^2 ||x-y||^2$?

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#inequality #hilbert-spaces #normed-spaces #inner-products
97
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Numerically robust Cauchy-Schwarz?

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#hilbert-spaces #inner-products #cauchy-schwarz-inequality
59
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A False Monomorphism from $\mathcal{L}(V)$ to $V'$

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#linear-algebra #vector-spaces #linear-transformations #inner-products
278
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Non-complete inner product spaces with orthonormal basis

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#inner-products
137
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True/false in linear algebra exam : inner product spaces

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#linear-algebra #inner-products
66
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Must $\langle x \mid x \rangle$ be real on a complex inner product space?

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#linear-algebra #complex-numbers #inner-products
21.8k
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Distinguishing between inner product and outer product in matrix notation

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#linear-algebra #inner-products #convention #outer-product
1k
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Inner product vs dot product on basis

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#linear-algebra #inner-products #change-of-basis
644
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Angle between vectors $\vec a + \vec b$ and $\vec c$?

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#vectors #inner-products
3.7k
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How to Express the Summation of an Inner Product Space

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#linear-algebra #summation #inner-products
137
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||x + y|| = 4 and ||x − y|| = 2. What is x · y? (Linear Algebra)

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#linear-algebra #normed-spaces #inner-products
69
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Why isn't the usual inner product defined for $P( \mathbb{R})$ valid for $C( \mathbb{R})$?

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#linear-algebra #inner-products
132
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Converse part of triangular inequality hold equality when third point lies in the both point

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#general-topology #metric-spaces #proof-explanation #inner-products
746
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Real Spectral Theorem: Sheldon Axler Proof

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#linear-algebra #proof-explanation #inner-products

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