### Basic Information

Fields# Definition and Examples, Finite Fields (modulo P), Complex Numbers and Polynomials in Complex Numbers, Matrices and Elementary Arithmetic Operations With Matrices, Elementary Line Operations And Elementary Matrices, Row Reduction. Systems of Linear Equations, Linear Spaces and Subspaces, The Subspace Spanned By a Set of Vectors And Linear Independence, Basis and Dimension of a Vector Space, Invertible Matrices, Change of Basis and Transformation Matrix Between Two Bases, Linear Transformations, Representative Matrix of A Linear Transformation and Matrix Similarity, Determinants, Eigenvalues and Eigenvectors, Diagonalization of Operators And Matrices