Lecture 4: Functions of Square Matrices
Functions of Scalars
Examples of functions of a scalar R:
f () = k ,
, e , ln ,
1
1
Can we dene functions of square matrices A Rnn ?
1
f (A) = Ak , A 2 , e A , ln(A), (In A)1
(Real) analytic functions: those f () th
Lecture 6: Quadratic Forms and Singular Value
Decomposition
Symmetric and Skew Symmetric Matrices
A Rnn is symmetric if AT = A.
Fact
For a symmetric matrix A, all of its eigenvalues are real, and all of its
eigenvectors are orthogonal.
Symmetric A can be
D EFINITE M ATRICES
I DENTIFYING DEFINITENESS AND SEMIDEFINITENESS
Econ 508-A
Denite Matrices
Carmen Astorne-Figari
Washington University in St. Louis
August 1, 2011
D EFINITENESS ON SUBSPACES
D EFINITE M ATRICES
I DENTIFYING DEFINITENESS AND SEMIDEFINITE