AI engineering glossary · Linear algebra
What is outer product?
Outer product (also called Tensor product of vectors): An operation that multiplies a column vector of length m by a row vector of length n to give an m x n matrix whose entry (i, j) is the i-th component times the j-th. Every outer product has rank one and is used in gradient updates and low-rank models.
Outer product: an example
[1, 2] as a column times [3, 4, 5] as a row gives [[3, 4, 5], [6, 8, 10]].
Related terms
More Linear algebra terms
- Permutation matrix
- Pivot
- Positive definite matrix
- Positive semi-definite matrix
- Power iteration
- Projection
- Projection matrix
- Pseudoinverse
Where you learn it
Outer product is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.