ECE 3093 Checklist

Part 1 - Andreas - Optimisation

Properties of Determinants
Eigenvalues and Eigenvectors calculation
Properties of Upper Triangular/Diagonal Matrices
Gaussian Elimination
Orthogonality (Q*lambda*QT)

Jordan Block - Generalized Eigenvectors
Schur Decomposition
QR Decomposition
Gram Schmidt Orthogonalisation
Power Methods (Basic, Shifted, Inverse) + Rayleigh Quotient
SVD - Fundamental Subspaces, Pseudo-inverse, rank
Condition Number, 2 norm
Linear Least Squares
Principle components
Solving constraints, global/local extrema
Hessian Matrix
Convexity
Steepest Descent Algorithm, Kantorovich Inequality

Part 2 - Daniel Mcinnes - Probability and Time Series

Basic Probability
Properties of Mean
Properties of Variance
Properties of Covariance
Properties of Covariance Matrices
Proofs of Standard Normal Mean and Variance

Markov and Chebychev Inequalities
Probability Distribution Table
Marginal, Joint Distributions
Independence and Uncorrelated Random Vectors
Cauchy-Schwarz Inequalities
Expecation and Covariance Matrices

Affine Mapping
Mapping X to Y, Distribution of Innovation
Density of f(x)
Spectral Decomposition
Minimal Representation

Best Linear Prediction - P(X|Y) : scalar and vector
Prediction Error - var(X-P(X|Y)) : scalar and vector
Confidence Interval

AR(p) Processes and Properties
MA(q) Processes and Properties
ARMA(p,q) Processes and Properties
Gaussian White Noise
ACVF properties
cov(Xt,Xt+h) properties
Power Transfer Function
Spectral Density

Backward Shift Operators (Finding Roots)
Stationarity and Causality of Linear Processes
Finding phi1, theta1, etc
Yule-Walker Method
Forecasting Operator : Pn(Xn+h), var(Xn - Pn(Xn+h))