Math244: Linear Algebra

Inner Product Spaces

• Definition of Inner Product
• Orthogonality
• Orthonormal Basis

Linear Transformations

• Basic Properties
• Kernel and Image of Linear Transformation
• Matrix of Linear Transformation

Eigenvalues and Eigenvectors & Diagonalization

 

-Eigenvalues and Eigenvectors

-Diagonalization

Matrices

• Matrices and Matrix Operations
• Elementary Row Operations
• Inverse of Matrix
• Special Matrices

Determinants

• Definition of Determinant
• Properties of Determinants
• The Adjoint Matrix

Systems of Linear Equations

• Gauss and Gauss–Jordan Methods
• Homogeneous systems of linear equations
• Cramer’s Rule

Vector Spaces

 

• Definition of a Vector Space
• Subspaces
• Linear Combination and Spanning Sets
• Linear Dependence & Linear Independence
• Basis and Dimension
• Coordinates and Change of Basis
• Rank of the Matrix