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Dot Product Derviation

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#euclidean-geometry #inner-products
290
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Riesz representative of gradient of $f(u) = u^*u$ in different inner products

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#linear-algebra #complex-numbers #hilbert-spaces #inner-products
10.8k
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Equivalence of integral kernels and basis transformations

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#integration #functional-analysis #inner-products #integral-transforms
54
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triangular inequality

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#linear-algebra #inner-products
39
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A vector in a function space

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#hilbert-spaces #inner-products
281
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Prove that $\sum_{i,j} \langle v_i, v_j \rangle \langle w_i, w_j \rangle \geq 0$

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#linear-algebra #inequality #inner-products
85
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$\|x\|=\|y\|$ implies that $\langle x+y,x-y\rangle=0$.

Published on
#functional-analysis #inner-products
484
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Do any books or articles develop basic Euclidean geometry from the perspective of "inner product affine spaces"?

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#geometry #reference-request #euclidean-geometry #inner-products #affine-geometry
57
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If $\mathrm{min}_{u\in U}||v-u||=||v-u_0||$, then $v-u_0\in U^{\perp}$

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#linear-algebra #inner-products
97
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If $d(x,z)=d(x,y)+d(y,z)$, then $z-x=t(y-x)$.

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#metric-spaces #inner-products
1.4k
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Inner product space of measures

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#measure-theory #hilbert-spaces #inner-products
333
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Intuitive meaning of orthogonality of linear transformations w.r.t Frobenius (H-S) inner product

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#linear-algebra #soft-question #inner-products
41
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Showing equivalence of inner products

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#inner-products
12.3k
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what is the difference between a Hermitian inner product and an inner product?

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#inner-products
12.4k
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Why are inner products defined to be linear in the first argument only?

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#linear-algebra #inner-products

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