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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 pencil method
The matrix pencil method is a numerical technique that estimates the poles and residues of damped complex exponentials from uniformly sampled data, widely used in signal processing and electromagnetics.
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.
Matroid intersection
Matroid intersection is the combinatorial optimization problem of finding a largest, or maximum-weight, set independent in two matroids on the same ground set, introduced by Jack Edmonds in 1970.
Matroid minor
A matroid minor is any matroid obtained from a matroid M by a sequence of deletions and contractions of elements, written M\D/C, paralleling graph minors and underlying the excluded-minor theory that characterizes minor-closed classes.
Matroid oracle
A matroid oracle is an abstract interface through which an algorithm accesses a matroid, most commonly an independence oracle that answers whether a given set is independent.
Matroid parity problem
The matroid parity problem, also called the matroid matching or matchoid problem, seeks a maximum-size independent set in a matroid whose elements are grouped into pairs.
Matroid representation
A matroid representation represents an abstract matroid as a matrix over a field whose linearly independent columns are exactly the matroid's independent sets; a matroid is representable when such a matrix exists.
Matroids and algebraic geometry
Matroids and algebraic geometry is the area where Hodge theory applied to matroid Chow rings proved log-concavity of characteristic-polynomial coefficients, resolving the Heron–Rota–Welsh conjecture, with tropical geometry linking matroids to linear spaces.
Max Newman
Max Newman (Maxwell Herman Alexander Newman, 1897–1984) was an English mathematician who led the Bletchley Park Newmanry breaking the Lorenz cipher and established the laboratory where the world's first stored-program computer ran in 1948.
Max-flow min-cut theorem
The max-flow min-cut theorem states that the maximum flow from source to sink in a network equals the minimum cut capacity, proved by Ford and Fulkerson in 1956.
Max-product algorithm
The max-product algorithm, also called min-sum or max-sum, is a message-passing method that computes the most probable assignment of a distribution over a factor graph, exactly on trees.
Max-stable distribution
A max-stable distribution is a probability distribution for which the maximum of independent, identically distributed copies, after rescaling and shifting, has again the same distribution; only three families qualify.
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.
Maximum a posteriori estimation
Maximum a posteriori (MAP) estimation is a Bayesian point-estimation method that picks the parameter value maximizing the posterior, equivalent to maximum likelihood with a prior added.
Maximum cardinality matching
A maximum cardinality matching, also known as a maximum matching, is a matching of largest possible size in a graph, a classic combinatorial optimization problem solvable in polynomial time.
Maximum entropy model
A maximum entropy model is a probability distribution chosen as the least-committal one consistent with observed constraints, selecting the distribution of largest entropy among those matching the data.
Maximum likelihood estimation
Maximum likelihood estimation (MLE) is a statistical estimation method that picks parameter values maximizing the likelihood of the observed data, introduced by R. A. Fisher in 1922.
Maximum principle
The maximum principle is a collection of theorems for elliptic and parabolic partial differential equations stating that a solution attains its extreme values on the boundary of its domain.
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.
Mayfly optimization algorithm
The mayfly optimization algorithm (MA) is a swarm-based metaheuristic introduced by Zervoudakis and Tsafarakis in 2020, combining particle swarm search with genetic crossover to optimize functions.
McDiarmid's inequality
McDiarmid's inequality, also called the bounded differences inequality, is a concentration inequality stating that functions of independent random variables with bounded coordinate changes concentrate around their mean.
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.