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Linear Algebra
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Introduction
Linear algebra
is a branch of mathematics concerned with the study of vectors, with families of vectors called vector spaces or linear spaces, and with functions that input one vector and output another, according to certain rules. These functions are called linear maps or linear transformations and are often represented by matrices. Linear algebra is central to modern mathematics and its applications. An elementary application of linear algebra is to the solution of a systems of linear equations in several unknowns. More advanced applications are ubiquitous, in areas as diverse as abstract algebra and functional analysis. Linear algebra has a concrete representation in analytic geometry and is generalized in operator theory. It has extensive applications in the natural sciences and the social sciences. Nonlinear mathematical models can often be approximated by linear ones.
Source:
Wikipedia.org
Formulas

Cartesian Coordinate

Cylindrical Coordinate

Spherical Coordinate

Transform from Cartesian to Cylindrical Coordinate

Transform from Cartesian to Spherical Coordinate

Transform from Cylindrical to Cartesian Coordinate

Transform from Spherical to Cartesian Coordinate

Divergence Theorem/Gauss' Theorem

Stokes' Theorem

Definition of a Matrix

Properties of Matrix Operations

Definition of Zero Matrix

Definition of Identity Matrix

Properties of the Identity Matrix

Definition of an Inverse of a Matrix

Properties of Inverse Matrices

Definition of the Determinant

Properties of Determinants

Definition of Triangular Matrices

Two Null Identities

Equality of Matrices

Elementary Matrices

Matrix Addition

Matrix Multiplication

Properties of Matrix Multiplication

Scalar Multiplication

The Transpose of a Matrix

Properties of Transposes

Gradient of a Scalar Field

Divergence of a Vector Field

Curl of a Vector Field
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