query: Proof of equivalence of algebraic and geometric dot product?
positive_passages.docid: 58958
positive_passages.text: How to understand dot product is the angle's cosine?
negative_passages.docid: 147111
negative_passages.text: Where is the Proof for the Sum-to-Product rule derrived from?
negative_passages.docid: 76020
negative_passages.text: What's the intuition for dot product?
negative_passages.docid: 131080
negative_passages.text: Geometric representation of the sum of a Geometric Series
negative_passages.docid: 22424
negative_passages.text: Has this "generalized semidirect product" been studied?
negative_passages.docid: 52973
negative_passages.text: The identity $(u\times v)\cdot(x\times y)=\begin{vmatrix}u\cdot x&v\cdot x\\ u\cdot y&v\cdot y\\\end{vmatrix}$
negative_passages.docid: 46703
negative_passages.text: Crash course on algebraic geometry with view to applications in physics
negative_passages.docid: 61666
negative_passages.text: Proving $ [(\vec{a}+\vec{b})\times(\vec{b}+\vec{c})]\cdot(\vec{c}+\vec{a})=2\vec{c}\cdot(\vec{b}\times\vec{a})$
negative_passages.docid: 122623
negative_passages.text: Geometric intuition for the tensor product of vector spaces
negative_passages.docid: 129986
negative_passages.text: Differential Geometry-Wedge product
negative_passages.docid: 91276
negative_passages.text: difference between dot product and inner product
negative_passages.docid: 112216
negative_passages.text: Geometric description of canonical commutation relation
negative_passages.docid: 16548
negative_passages.text: Prove $(x+y) \text{ mod } n = ((x \text{ mod } n)+(y \text{ mod } n)) \text{ mod } n,\,$ and product analog
negative_passages.docid: 30678
negative_passages.text: Direct proof that the wedge product preserves integral cohomology classes?
negative_passages.docid: 85039
negative_passages.text: Purely "algebraic" proof of Young's Inequality
negative_passages.docid: 155537
negative_passages.text: Intuition of the cyclic trace property of matrix products and relation to the determinant?
negative_passages.docid: 51018
negative_passages.text: Proof of proposition 5.3.1 of Ravi Vakil's notes on algebraic geometry