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In linear algebra, the outer product of two coordinate vectors is the matrix whose entries are all products of an element in the first vector with an element in the second vector. If the two coordinate vectors have dimensions n and m , then their outer product is an n × m matrix.
The product in the algebra is called the geometric product, and the product in the contained exterior algebra is called the exterior product (frequently called the wedge product or the outer product [d]).
The cross product u × v can be interpreted as a vector which is perpendicular to both u and v and whose magnitude is equal to the area of the parallelogram determined by the two vectors. It can also be interpreted as the vector consisting of the minors of the matrix with columns u and v. The triple product of u, v, and w is geometrically a ...
the outer product of two column vectors and is denoted and defined as or , where means transpose, the tensor product of two ...
The tensor product, outer product and Kronecker product all convey the same general idea. The differences between these are that the Kronecker product is just a tensor product of matrices, with respect to a previously-fixed basis, whereas the tensor product is usually given in its intrinsic definition .
The resulting matrix, known as the matrix product, ... Outer product, also called dyadic product or tensor product of two column matrices, which is ...
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For a finite-dimensional vector space, the outer product can be understood as simple matrix multiplication: | | () = The outer product is an N × N matrix, as expected for a linear operator. One of the uses of the outer product is to construct projection operators .