Bilinear maps | Operations on vectors

Outer product

In linear algebra, the outer product of two coordinate vectors is a matrix. If the two vectors have dimensions n and m, then their outer product is an n × m matrix. More generally, given two tensors (multidimensional arrays of numbers), their outer product is a tensor. The outer product of tensors is also referred to as their tensor product, and can be used to define the tensor algebra. The outer product contrasts with: * The dot product (a special case of "inner product"), which takes a pair of coordinate vectors as input and produces a scalar * The Kronecker product, which takes a pair of matrices as input and produces a block matrix * Standard matrix multiplication (Wikipedia).

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Inner products (video 3): Definition

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From playlist Inner Products

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Inner products (video 8): Outro

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From playlist Inner Products

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Inner Products (video 7): Unconventional Inner Products

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From playlist Inner Products

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Inner Products (video 4): Lengths and Distances, Part 1/2

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From playlist Inner Products

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From playlist Matrix Algebra for Engineers

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Inner Products (video 6): Angles and Orthogonality

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From playlist Inner Products

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Inner Products (video 2): Dot Product

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From playlist Inner Products

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From playlist Factoring Trinomials with a Leading Coefficient Not 1

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From playlist Factoring Trinomials with a Leading Coefficient Not 1

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Norm (mathematics) | Vectorization (mathematics) | Signal processing | NumPy | Spinors in three dimensions | Scatter matrix | Vector space | Linear algebra | Tensor product | Trace (linear algebra) | Élie Cartan | Dot product | Matrix norm | Coordinate vector | Determinant | Conjugate transpose | Dyadics | Hadamard product (matrices) | Binary relation | Tensor algebra | Householder transformation | Commutative property | Dual space | Cartesian product | Wolfram Mathematica | Scalar (mathematics) | Cross product | Complex conjugate | Logical matrix | Kronecker product | Ricci calculus | Transpose | Matrix multiplication | Inner product space | Bra–ket notation | Matrix (mathematics) | Rank (linear algebra) | Exterior product | Eigendecomposition of a matrix