Linear Algebra

Linear Algebra for college & university students. Contains vector calculus / spaces, matrices and matrix calculus, inner product spaces, and more.

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Course content

Complex numbers

Introduction to Complex numbers

Calculating with complex numbers

Complex functions

Complex polynomials

Differential equations and Laplace transforms

Vector calculus in plane and space

Vectors in Planes and Space

Straight Lines and Planes

Bases, Coordinates and Equations

Distances, Angles and Inner Product

The Cross Product

Systems of linear equations and matrices

Linear equations

Systems of Linear Equations

Systems and matrices

Matrices

Conclusion of Systems of linear equations and matrices

Vector spaces

Vector spaces and linear subspaces

Spans

More about subspaces

Coordinates

Inner Product Spaces

Inner product, length, and angle

Orthonormal systems

Orthogonal projections

Complex inner product spaces

Linear maps

Linear maps

Matrices of Linear Maps

Dual vector spaces

Matrix calculus

Rank and inverse of a matrix

Determinants

Matrices and coordinate transformations

Minimal polynomial

Invariant subspaces of linear maps

Eigenvalues and eigenvectors

Diagonalizability

Invariant subspaces

Matrices and coordinate transformations

Orthogonal and symmetric maps

Orthogonal maps

Classification of orthogonal maps

Isometries

Unitary maps

Symmetric maps

Applications of symmetric maps

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