query: Generalizing Cauchy-Schwarz for more than two vectors
positive_passages.docid: 152932
positive_passages.text: Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$
negative_passages.docid: 19497
negative_passages.text: Analogue of spherical coordinates in $n$-dimensions
negative_passages.docid: 29172
negative_passages.text: Use Cauchy-Schwarz inequality to show series convergence
negative_passages.docid: 66151
negative_passages.text: Solving inequality for convex functions.
negative_passages.docid: 146656
negative_passages.text: Multivariate Application of Slutsky's lemma
negative_passages.docid: 75694
negative_passages.text: The Schwarz Reflection Principle for a circle
negative_passages.docid: 82625
negative_passages.text: How do I prove this using question using Cauchy-Schwarz inequality?
negative_passages.docid: 111443
negative_passages.text: Optimization of $2x+3y+z$ under the constraint $x^2+ y^2+ z^2= 1$
negative_passages.docid: 82823
negative_passages.text: Attractive Boxed Equations
negative_passages.docid: 16293
negative_passages.text: N-dimensional generalization of vector curl from elements of Jacobian
negative_passages.docid: 82198
negative_passages.text: Proving Convexity of Multivariate Function using Conditional Univariate Convexity
negative_passages.docid: 61710
negative_passages.text: Proof of Cauchy-Schwarz inequality - Why select s so that so that $||x-sy||$ would be minimized?
negative_passages.docid: 76155
negative_passages.text: Verification of extension result for Lipschitz functions
negative_passages.docid: 51313
negative_passages.text: Extension of linearly independent set to a basis in an infinite dimensional vector space
negative_passages.docid: 28511
negative_passages.text: Hypervolume of a $N$-dimensional ball in $p$-norm
negative_passages.docid: 94256
negative_passages.text: Partial factorization of multivariate polynomials in terms of given polynomials
negative_passages.docid: 88013
negative_passages.text: injective linear transformation basis.