AI engineering glossary · Linear algebra
What is quadratic form?
Quadratic form: An expression x^T A x that turns a vector into a single number by multiplying its components in pairs with weights from a matrix. It describes the shape of quadratic loss surfaces, and its sign pattern shows whether they curve up or down.
Quadratic form: an example
For A = [[1,0],[0,4]], x^T A x = x1^2 + 4*x2^2, so x = [2, 1] gives 8.
Related terms
More Linear algebra terms
- Rank
- Rank-nullity theorem
- Rank-one matrix
- Reduced row echelon form
- Rotation matrix
- Row echelon form
- Row space
- Row vector
Where you learn it
Quadratic form is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.