Matrices and Decompositions

In this chapter we present important propoerties of matrices and their decompositions.

• Rank of a Matrix
• Determinant
• Gaussian Elimination and the PLU Decomposition
• Fundamental Equivalences for Square matrices
• Trace
• Eigenvalues and Eigenvectors
• Orthogonal matrices
• Symmetric matrices
• Rayleigh Quotients
• Matrix Norms
• Positive (semi-)definite matrices
• Principal Components Analysis
• Singular value decomposition
• Moore-Penrose Pseudoinverse
• Orthogonal projections
• Fundamental Subspaces