ADVANCED ALGEBRA

Polynomial;Division Algorithm;Greatest Common Divisor;Least Common Multiple;Euclidean Algorithm;Chinese Remainder Theorem;Fundamental Theorem of Algebra;Schönemann–Eisenstein Criterion;Descartes' Rule of Signs;Sturm's Theorem;Symmetric Polynomial;Determinant;Laplace Expansion;Cramer's Rule;Matrix;Rank of a Matrix;Elementary Operation;Equivalence of Matrices;Cauchy–Binet Formula;System of Linear Equations;Linear Dependence;Structure of Solutions;Linear Space;Dimension Formula;Linear Map;Matrix Representation of a Linear Map;Similarity of Matrices;Eigenvalue;Eigenvector;Characteristic Polynomial;Cayley–Hamilton Theorem;Diagonalization of Matrices;Λ-Matrix;Smith Normal Form;Determinantal Divisor;Invariant Factor;Elementary Divisor;Rational Canonical Form;Jordan Canonical Form;Quadratic Form;Congruence of Matrices;Law of Inertia;Inner Product Space;Euclidean Space;Orthogonal Transformation;Rotation;Singular Value Decomposition;Moore-Penrose Inverse;Unitary Space;Eigenvector-Eigenvalue Identity;Bilinear Form;Quadratic Space;Symplectic Space