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If the two coordinate 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.
Download QR code; Print/export Download as PDF; Printable version; In other projects ... Here, is the outer product of two vectors and . The general form shown here ...
Download QR code; Print/export Download as PDF; Printable version; In other projects ... (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 ...
Download QR code; Print/export Download as PDF; Printable version; In other projects ... Specifically, for the outer product of two vectors, ...
The determinant of the left hand side is the product of the determinants of the three matrices. Since the first and third matrix are triangular matrices with unit diagonal, their determinants are just 1. The determinant of the middle matrix is our desired value. The determinant of the right hand side is simply (1 + v T u). So we have the result:
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Download as PDF; Printable version ... this transformation can be expressed in terms of an outer product as: = ... of a matrix is the product of its ...