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Gradients of Functions from Matrices to Scalars
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Classroom Contents
Matrix Calculus for Linear Algebra - MIT 18.06 Spring 2020
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- 1 Matrix Calculus
- 2 Scalar Calculus
- 3 Emphasis on Linearization
- 4 Gradients
- 5 Geometrically
- 6 Matrix/Vector Product Rule
- 7 Gradients the straightforward but klunky way
- 8 Gradients the sophisticated way
- 9 Example f(x) = (Ax-b)'(Ax-b)
- 10 Gradient Notation
- 11 The Trace
- 12 Linear Functions of Matrices
- 13 Gradients of Functions from Matrices to Scalars
- 14 Vector to Vector Jacobians
- 15 How are Gradients Used
- 16 The Jacobian Matrix, vectors to vectors
- 17 A Key Point -- you don't have to write out the matrix elements
- 18 relationship to volumes
- 19 Matrices to Matrices
- 20 Derivatives of Matrix to Matrix Functions
