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New posts in inner-products
Motive for the definition of inner product
logic
definition
inner-products
philosophy
If the unit sphere of a normed space is homogeneous is the space an inner product space?
normed-spaces
inner-products
How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)
linear-algebra
inner-products
orthogonality
Verfication of deduction made using the Cauchy-Schwarz inequality
inequality
proof-verification
inner-products
cauchy-schwarz-inequality
When does an inner product induce a norm?
linear-algebra
normed-spaces
inner-products
Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$
linear-algebra
abstract-algebra
vector-spaces
determinant
inner-products
Matrix given by $a_{ij} = 1/(i+j)$ is non-singular.
linear-algebra
determinant
inner-products
If $M$ is a closed subspace of an Hilbert space $H$, then $M^{\perp\perp}=M$
hilbert-spaces
inner-products
orthogonality
Are there any "other" ways to show a normed space is NOT an inner product space?
normed-spaces
inner-products
If the inner product induces the l2 norm, what kind of non-inner product induces a general Lp norm where $p \neq 2$?
normed-spaces
lp-spaces
inner-products
Can we infer that $\text{Im}(P)=S$ if $\Vert P(x)-x\Vert =\min\big\{\Vert y-x\Vert :y\in S\big\}$ for all $x\in H$? [closed]
functional-analysis
analysis
hilbert-spaces
inner-products
Is every normed vector space, an inner product space
normed-spaces
inner-products
Necessity of completeness of the inner product space in Riesz representation theorem
functional-analysis
analysis
examples-counterexamples
inner-products
riesz-representation-theorem
A problem with inner products on Hilbert space
functional-analysis
hilbert-spaces
inner-products
Finding $T^{\perp}$!
hilbert-spaces
inner-products
orthogonality
With inner product $\langle f,g\rangle=\int_0^{2\pi}f(t)\overline{g(t)}dt$ on $L_2[0,2\pi]$ how do $||f||$, $||f||_2$ and $\langle f,f\rangle$ relate?
normed-spaces
inner-products
Angle between subspaces of inner product space
inner-products
Is a norm a continuous function?
general-topology
inner-products
normed-spaces
Equivalent inner products on a Hilbert space
functional-analysis
hilbert-spaces
inner-products
prove that a function is an inner product
linear-algebra
normed-spaces
inner-products
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