outer product

Noun

Meaning

outer product (plural outer products)

(mathematics, linear algebra) The tensor product of two vectors.

Synonyms

Examples

It is not the outer product of linear algebra. Source: Internet

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. Source: Internet

Extensions of the inner and outer products It is common practice to extend the outer product on vectors to the entire algebra. Source: Internet

If the dimensions are the same, then the inner product is the trace of the outer product (trace only being properly defined for square matrices). Source: Internet

In other words, the geometric product of two distinct vectors is completely specified by their outer product, or more generally : Therefore, every blade of grade r can be written as a geometric product of r vectors. Source: Internet

Note that the outer product is defined for different dimensions, while the inner product requires the same dimension. Source: Internet

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