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.

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

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

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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.

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

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

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

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

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

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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.

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