# Outer product

## Vector operation / From Wikipedia, the free encyclopedia

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Not to be confused with Exterior product.

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. 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