Physical world and mathematics

Mathieu Orfila

Mathieu Orfila, full name Mateu Josep Bonaventura Orfila i Rotger (1787–1853), was a Spanish-born, French-naturalized physician and chemist regarded as the father of modern toxicology.

MathOverflow

MathOverflow is a question and answer site for professional mathematicians, focused on current research in mathematics, founded in 2009 and hosted on the Stack Exchange network since 2013.

Sep 21, 2026

Matias Zaldarriaga

Matias Zaldarriaga, born 1971 in Buenos Aires, is an Argentine-born cosmologist and Richard Black Professor at the Institute for Advanced Study, known for his 1997 CMB polarization work.

Matilda effect

The Matilda effect is the systematic under-recognition of women in science, named by historian Margaret Rossiter in 1993 for suffragist Matilda Joslyn Gage, as a counterpart to the Matthew effect.

Matric potential

Matric potential, also called soil-water tension, is the part of soil water potential due to capillary and adsorptive forces, becoming more negative as soil dries.

Matrix

A matrix is a rectangular array of numbers arranged in rows and columns, the central object of linear algebra, used to represent linear transformations and systems of equations.

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, 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 effect

A matrix effect is an alteration of an analyte's response in a mass spectrometric assay caused by interfering, often unidentified sample matrix components, most commonly seen in LC-MS as ion suppression or enhancement.

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 isolation

Matrix isolation is a sample-preparation technique that dilutes reactive or unstable molecules in an inert matrix, usually solid argon or nitrogen, at cryogenic temperature so their structure can be identified by spectroscopy.

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 mechanics

Matrix mechanics, also known as Heisenberg matrix mechanics, is the first complete formulation of quantum mechanics, developed in 1925, representing observables like position and momentum by noncommuting Hermitian matrices.

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 polarimetry

Matrix polarimetry is an optical measurement technique that determines a sample's full polarization response by measuring its 4×4 Mueller matrix, used in microscopy and materials characterization.

Matrix product state

A matrix product state (MPS) represents a quantum many-body wave function as a one-dimensional chain of small tensors, one per lattice site, and underlies the density-matrix renormalization group.

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.

Matrix solid-phase dispersion

Matrix solid-phase dispersion is an extraction technique in analytical chemistry in which a solid or semi-solid sample is blended with an abrasive sorbent and analytes are recovered by solvent elution.

Matrix theory (M-theory)

Matrix theory, also called the BFSS matrix model, is a conjectured nonperturbative definition of M-theory, proposed by Banks, Fischler, Shenker, and Susskind in October 1996.

Matrix-assisted laser desorption/ionization

Matrix-assisted laser desorption/ionization (MALDI) is a soft ionization technique in mass spectrometry, introduced in 1987 by Karas and coworkers and most often coupled to time-of-flight analysis of proteins, peptides, and polymers.

Matrix-assisted laser desorption/ionization mass spectrometry imaging

Matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI-MSI) is a label-free technique that maps molecules, from lipids to proteins, across tissue sections, first demonstrated by Caprioli in 1997 and used in drug and cancer research.