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Summary Of: Dot product

The dot product of two vectors... the dot product of two three... vectors the dot product is defined as... The dot product is typically applied to vectors from... the dot product can also be written as... the dot product of the two above... their dot product simply gives the cosine of the angle between them... This property of the dot product has several useful applications... The dot product is also a scalar in this sense... the dot product does not obey the... the dot product is invariant under isometric changes of the basis... the dot product is invariant under a... so we conclude that taking the dot product of a vector... necessary and the inner product coincides with the dot product as defined above... Explanation of dot product including with complex vectors...

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Inner product space | mathematics | vectors | real numbers | scalar | inner product | orthonormal | Euclidean space | summation notation | complex | complex conjugate | orthonormal | vector spaces | below | matrix multiplication | matrices | column matrices | transpose | row matrix | The dot product A • B is equal to |A| |B| cos(θ). |A| cos(θ) is the scalar projection of A onto B | | scalar projection | length | angle | length | angle | cosine | orthogonal | if and only if | basis | orthonormal | unit vectors | unit vector | scalar projection | scalar component | rotation | rotation matrix | matrix multiplication | orthonormal bases | row vector | column vector | physics | scalar | physical quantity | product | numerical value | physical unit | Mechanical work | force | displacement | vectors | scalar | commutative | distributive | bilinear | perpendicular | if and only if | cancellation law | distributive law | coordinate transformation | orthogonal matrix | Triple product | cross-products | physics | Pythagorean theorem | Lemma | law of cosines | distributive law | Q.E.D. | inner product | abstract vector spaces | norm | inner product space | orthogonal | Frobenius inner product | square matrix | matrix multiplication | basis set | orthogonal | unit vectors | orthonormal basis | identity matrix | Cross product | Matrix multiplication | Cauchy–Schwarz inequality | Eric W. Weisstein | MathWorld | The Wolfram Demonstrations Project | v | d | linear algebra | Scalar | Vector | Vector space | Vector resolute | Linear span | Linear map | Linear independence | Linear combination | Basis | Column space | Row space | Dual space | Orthogonality | Rank | Minor | Kernel (matrix) | Eigenvalue, eigenvector and eigenspace | Least squares regressions | Outer product | Inner product space | Cross product | Transpose | Gram–Schmidt process | Matrix decomposition | Categories | Linear algebra | Binary operations | Articles containing proofs | Vectors |
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Dot product".