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Matrix (mathematics)
A matrix is a rectangular array of numbers arranged in rows and columns, treated as a single mathematical object; James Joseph Sylvester first used the term in 1850.
Matrix calculus
Matrix calculus, also called matrix differentiation, extends differential calculus to functions whose arguments or values are vectors or matrices, and is central to statistics, econometrics, and machine learning.
Matrix completion
Matrix completion is the problem of recovering an unknown low-rank matrix from a small sample of its entries, famously applied in the Netflix Prize recommender competition.
Matrix decomposition
A matrix decomposition, or matrix factorization, represents a matrix as a product of simpler matrices such as LU, Cholesky, QR, and the singular value decomposition.
Matrix exponential
The matrix exponential, or exponential of a matrix, generalizes the scalar exponential to square matrices via a convergent power series and gives the closed-form solution of linear differential systems.
Matrix function
A matrix function extends a scalar function such as the exponential, logarithm, sine, or square root to a square matrix, defined through the matrix's eigenstructure rather than applied to each entry.
Matrix logarithm
The matrix logarithm of a square matrix A is any matrix X whose matrix exponential is A, so e^X = A. It need not exist or be unique.
Matrix multiplication
Matrix multiplication combines two matrices into a third, each entry a dot product of a row with a column; it is not commutative and costs O(n³) operations.
Matrix norm
A matrix norm assigns each matrix a nonnegative size under the norm axioms, measuring how much it can amplify a vector and underpinning error analysis and condition numbers.
Matrix pencil
A matrix pencil is the family of matrices A − λB for same-size matrices A and B, central to the generalized eigenvalue problem Ax = λBx.
Matrix similarity
Matrix similarity, also called matrix conjugation or similarity transformation, is a relation between square matrices of the same order: A and B are similar when B = S⁻¹AS for some invertible S.
Matroid
A matroid, also called a combinatorial pregeometry, is a combinatorial structure abstracting linear independence in vector spaces and cycle-freedom in graphs, introduced by Hassler Whitney in 1935.
Maximal ideal
A maximal ideal is a proper ideal of a ring with no ideal strictly between it and the ring; an ideal is maximal exactly when the quotient ring is a field.
Maya numerals
Maya numerals, also called Mayan numerals, are the number symbols of the ancient Maya, a base-20 system using dots, bars, and a shell glyph for zero.
McKay correspondence
The McKay correspondence, first observed by John McKay in 1980, links finite subgroups of SU(2) to affine ADE Dynkin diagrams via the irreducible representations of each group.
McKay graph
The McKay graph, or McKay quiver, is a graph encoding how a finite group's irreducible representations combine by tensor product with a chosen representation, introduced by John McKay around 1980.
McLaughlin group
The McLaughlin group (McL) is one of the 26 sporadic finite simple groups, of order 898,128,000, discovered by Jack McLaughlin in 1969 and tied to the Leech lattice and the McLaughlin graph on 275 vertices.
Measure algebra
A measure algebra is a Boolean σ-algebra with a strictly positive measure, built from measurable sets identified when they differ only by a set of measure zero.
Mechanical calculator
A mechanical calculator, or calculating machine, performs arithmetic using gears and drums rather than electronics; first built in 1623, it was displaced by electronic calculators in the 1960s.
Mellin transform
The Mellin transform is an integral transform converting a function on the positive real axis into a function of a complex variable, the multiplicative counterpart of the Fourier transform.
Mental calculation
Mental calculation, also known as mental arithmetic or mental math, is the solving of arithmetic problems entirely in the head without aids such as a calculator or pen and paper.
Mersenne prime
A Mersenne prime is a prime number of the form 2^p − 1, named after Marin Mersenne. The largest known prime, found in 2024, is one.
Mersenne primes
Mersenne primes are prime numbers of the form 2^p − 1 with p prime, named for Marin Mersenne; 52 are known, and they correspond to even perfect numbers.
Mertens function
The Mertens function, M(x) = Σ μ(n), sums the Möbius function up to x. Mertens conjectured |M(x)| < √x in 1897; Odlyzko and te Riele disproved it in 1985.
Metric Diophantine approximation
Metric Diophantine approximation is the branch of number theory that classifies, by Lebesgue measure, which real numbers admit infinitely many rational approximations of a prescribed quality.
Michael Scot
Michael Scot, also known as Michael the Scot, was a Scottish translator and astrologer who served Emperor Frederick II and translated Aristotle from Arabic into Latin.
Miller–Rabin primality test
The Miller–Rabin primality test is a randomized algorithm deciding whether an odd integer is prime; introduced by Gary Miller in 1976 and made unconditional by Michael Rabin in 1980.
Milnor K-theory
Milnor K-theory is a graded ring K*M(F) attached to a field F, introduced by John Milnor in 1970, with its degree-two part recovering the classical group K2(F).
Min-max theorem
The min-max theorem, usually called the Courant–Fischer theorem, is a linear algebra result stating that every eigenvalue of a Hermitian matrix solves a min-max problem over subspaces using the Rayleigh quotient.
Minimal model (physics)
Minimal model, also called Virasoro minimal model, is a two-dimensional conformal field theory with only finitely many primary fields, introduced by Belavin, Polyakov, and Zamolodchikov in 1984.