Linear Algebra

• Linear dependence and independence — T3
• Subspaces — T2
• Bases and dimension; coordinates in a basis — T2
• Linear transformations — T3
• Rank and nullity; rank-nullity theorem — T2
• Matrix of a linear transformation — T1
• Algebra of matrices — T3
• Row and Column Reduction; Echelon Form — T4
• Congruence and similarity of matrices — T3
• Rank of a matrix — T2
• Inverse of a matrix (adjoint and row reduction) — T3
• Solution of system of linear equations — T2
• Eigenvalues and eigenvectors — T1
• Cayley-Hamilton theorem — T3
• Diagonalization via Eigenvectors — T4
• Symmetric and Skew-Symmetric Matrices — T4
• Hermitian and skew-Hermitian matrices — T3
• Orthogonal and unitary matrices — T3
• Quotient Vector Space V/W — T4