Matrix Inner Product Math

Simply in coordinates the inner product is the product of a 1 n covector with an n 1 vector yielding a 1 1 matrix a scalar while the outer product is the product of an m 1 vector with a 1 n covector yielding an m n matrix. Finding the product of two matrices in addition to multiplying a matrix by a scalar we can multiply two matrices. The inner product between two vectors is an abstract concept used to derive some of the most useful results in linear algebra as well as nice solutions to several difficult practical problems.

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Definition of an inner and outer product of two column vectors.

Matrix inner product math. Join me on coursera. Note that the outer product is defined for different dimensions while the inner product requires the same dimension. The term inner product is opposed to outer product which is a slightly more general opposite. It is unfortunately a pretty unintuitive concept although in certain cases we can interpret it as a measure of the similarity between two vectors.

Finding the product of two matrices is only possible when the inner dimensions are the same meaning that the number of columns of the first matrix is equal to the number of rows of the second matrix.