Matrix Calculus for Linear Algebra - MIT 18.06 Spring 2020

This course introduces matrix calculus through linearization, gradients, Jacobians, trace notation, and derivatives of matrix-valued functions. It includes geometric interpretations and examples such as the gradient of a quadratic function.

Syllabus

Matrix Calculus.
Scalar Calculus.
Emphasis on Linearization.
Gradients.
Geometrically.
Matrix/Vector Product Rule.
Gradients the straightforward but klunky way.
Gradients the sophisticated way.
Example f(x) = (Ax-b)'(Ax-b).
Gradient Notation.
The Trace.
Linear Functions of Matrices.
Gradients of Functions from Matrices to Scalars.
Vector to Vector Jacobians.
How are Gradients Used.
The Jacobian Matrix, vectors to vectors.
A Key Point -- you don't have to write out the matrix elements.
relationship to volumes.
Matrices to Matrices.
Derivatives of Matrix to Matrix Functions.