query: Prove that $f(x,y)$ defines an inner product
positive_passages.docid: 57619
positive_passages.text: Norms Induced by Inner Products and the Parallelogram Law
negative_passages.docid: 118996
negative_passages.text: Prove that $T$ is an orthogonal projection
negative_passages.docid: 83023
negative_passages.text: From axiom of regularity, how can I prove $x \notin y \lor y \notin x$
negative_passages.docid: 32359
negative_passages.text: Inner product of two continuous maps is continuous
negative_passages.docid: 78698
negative_passages.text: Prove if $f$ has a right inverse function: $f\circ g=id_x$ $\iff$ $f$ is onto $Y$
negative_passages.docid: 131232
negative_passages.text: Simplifying the expression of a product of inner products
negative_passages.docid: 30569
negative_passages.text: Prove that the only operator on $\mathbb{C}$ for which his inner product is zero is zero
negative_passages.docid: 75614
negative_passages.text: Proving that $n|m\implies f_n|f_m$
negative_passages.docid: 83970
negative_passages.text: Proof of an elementary property of Projection Operators
negative_passages.docid: 108704
negative_passages.text: Help with proof of $|x+y| \geq |x|-|y|$
negative_passages.docid: 130537
negative_passages.text: Proving that $d(f,g)=\|f-g\| = \sup \limits_{0\leq x \leq 1} |f(x)-g(x)|$ is a metric on $X=C[0,1]$
negative_passages.docid: 149354
negative_passages.text: Proof of continuity $f(x+y) = f(x) + f(y)$
negative_passages.docid: 70475
negative_passages.text: Proving a basis for inner product space V when $||e_j-v_j||< \frac{1}{\sqrt{n}}$.
negative_passages.docid: 21391
negative_passages.text: Proving Functions are Surjective
negative_passages.docid: 118207
negative_passages.text: Prove that the product of two continuous functions is continuous
negative_passages.docid: 91947
negative_passages.text: Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
negative_passages.docid: 128985
negative_passages.text: Show that $\langle x,y\rangle_A = \langle Ax,Ay\rangle$ is an inner product on $\mathbb R^n$