Mathematics

A mathematical expression consisting of variables, coefficients, and exponents combined using addition, subtraction, and multiplication. The highest exponent in a polynomial determines its degree.

A rectangular array of numbers arranged in rows and columns, commonly used to solve systems of equations, perform transformations, and represent data.

A special number associated with a square matrix, calculated using a specific formula, which helps determine if the matrix has an inverse.

A scalar that describes how a linear transformation changes a vector's magnitude along certain directions. It is found by solving the characteristic equation of a matrix.

A set with an operation that satisfies four properties: closure, associativity, identity element, and invertibility.

An algebraic structure with two operations, usually addition and multiplication, where addition forms a group, and multiplication is associative.

A mathematical system where addition, subtraction, multiplication, and division (except by zero) can be performed, with all operations following specific properties.

The process of breaking down an algebraic expression or number into simpler factors, often to simplify equations or find roots.

A function between two algebraic structures that preserves their operations, meaning the function maintains structure consistency.

A property where the order of applying an operation does not affect the result. This property holds for addition and multiplication but not for matrix multiplication.