21
Linear functions
Lecture 2
Linear functions
EE263
linear equations and functions
engineering examples
interpretations
Autumn 2003
22
Linear functions
Linear equations
consider system of linear equations
y1 = a11x1 + a12x2 + + a1nxn
y2 = a21x1 + a22x
Autonomous linear dynamical systems
71
Lecture 7
Autonomous linear dynamical systems
EE263
autonomous linear dynamical systems
examples
higher order systems
linearization near equilibrium point
linearization along trajectory
Autumn 2003
72
Autonomous
81
Solution via Laplace transform and matrix exponential
Lecture 8
Solution via Laplace transform and
matrix exponential
EE263
Laplace transform
solving x = Ax via Laplace transform
state transition matrix
matrix exponential
qualitative behavior and
Weighted least squares
Iteratively reweighted least squares
Weighted least squares
Example: heteroscedastic errors
Weighted least squares
Weighted least squares
Example: heteroscedastic errors
Iteratively reweighted least squares
Iteratively reweighted le
Orthonormal vectors and QR factorization
41
Lecture 4
Orthonormal vectors and QR
factorization
EE263
Autumn 2003
orthonormal vectors
Gram-Schmidt procedure, QR factorization
orthogonal decomposition induced by a matrix
Orthonormal vectors and QR factor
Jordan canonical form
10 1
Lecture 10
Jordan canonical form
EE263
Jordan canonical form
generalized modes
Cayley-Hamilton theorem
Autumn 2003
10 2
Jordan canonical form
Jordan canonical form
what if A cannot be diagonalized?
any matrix A Rnn can be put