Area
Algebra
79 concepts in 14 topics and 3 courses. Explore freely or follow a guided course.
79concepts
14topics
3courses
Courses
Modern algebra
Linear algebra
Systems and matrices 6 · Determinants 4 · Vector spaces 7 · Linear transformations 5 · Eigenvalues and eigenvectors 4 · Orthogonality 5
Modern algebra I
Group theory 9 · Groups and subgroups 8 · Cosets and quotients 8 · Actions and Sylow theorems 8 · Special groups 3 · Rings and domains 4 · Polynomials and fields 7
Topics
Lie theory 1 concepts
Systems and matrices 6 concepts
System of linear equations · Matrix · Matrix multiplication · Gaussian elimination · Inverse matrix · Transpose matrix
Determinants 4 concepts
Determinant · Cofactor and Laplace expansion · Properties of the determinant · Cramer's rule
Vector spaces 7 concepts
Vector in ℝⁿ · Vector space · Vector subspace · Linear combination and span · Linear independence · Basis and dimension · Rank of a matrix
Linear transformations 5 concepts
Linear transformation · Matrix of a linear transformation · Kernel and image · Rank–nullity theorem · Change of basis
Eigenvalues and eigenvectors 4 concepts
Eigenvalue and eigenvector · Characteristic polynomial · Eigenspace · Diagonalization
Orthogonality 5 concepts
Dot product · Vector norm · Orthogonal vectors · Orthogonal projection · Gram–Schmidt process
Group theory 9 concepts
Set · Subset · Cartesian product · Function · Binary operation · Group · Identity element · Inverse element · Abelian group
Groups and subgroups 8 concepts
Subgroup · Order of a group · Order of an element · Generated subgroup · Cyclic group · Center of a group · Group homomorphism · Group isomorphism
Cosets and quotients 8 concepts
Kernel of a homomorphism · Coset · Index of a subgroup · Lagrange's theorem · Normal subgroup · Quotient group · First isomorphism theorem · Direct product of groups
Actions and Sylow theorems 8 concepts
Symmetric group · Cycle of a permutation · Sign of a permutation · Group action · Orbit-stabilizer theorem · Orbit and stabilizer · p-group · Sylow theorems
Special groups 3 concepts
Classification of finite abelian groups · Dihedral group · Simple group
Rings and domains 4 concepts
Unit of a ring · Zero divisor · Characteristic of a ring · First isomorphism theorem for rings
Polynomials and fields 7 concepts
Polynomial ring · Polynomial division algorithm · Euclidean domain · Irreducible element · Unique factorization domain · Field of fractions · Greatest common divisor