6,052 articles
Pseudospectrum
A pseudospectrum is a family of sets in the complex plane attached to a matrix or operator, showing where the resolvent norm is large, which matters most for non-normal operators.
PSPACE
PSPACE is the complexity class of decision problems decidable using polynomial memory regardless of time; it contains P and NP, and Savitch's theorem shows nondeterminism adds nothing.
Puiseux series
A Puiseux series is a power series in fractional powers of a variable that expresses the local behavior of algebraic functions; the method goes back to Newton.
Pullback (category theory)
A pullback, also called the fibered product, is the limit in category theory of two morphisms with a common codomain; in sets it is the set of pairs (a, b) with f(a) = g(b).
Pumping lemma for context-free languages
The pumping lemma for context-free languages, also called the Bar-Hillel lemma, is a theorem proved by Bar-Hillel, Perles, and Shamir in 1961, used chiefly to prove languages are not context-free.
Pumping lemma for regular languages
The pumping lemma for regular languages, stated by Bar-Hillel, Perles, and Shamir in 1961, says long strings of a regular language can be pumped and stays used to prove non-regularity.
Pure mathematics
Pure mathematics is mathematics pursued for its own sake rather than immediate application, covering fields like algebra, number theory, and analysis, whose results often become applied later.
Pure-jump Lévy process
A pure-jump Lévy process is a Lévy process whose Gaussian (Brownian) component is absent, so all randomness enters through jumps; examples include the variance gamma, NIG, and CGMY processes.
Push–relabel maximum flow algorithm
The push–relabel maximum flow algorithm, also known as the push–relabel algorithm or preflow push, is a maximum flow algorithm introduced by Goldberg and Tarjan in 1988.
Pushdown automaton
A pushdown automaton (PDA) is a finite-state machine with a stack as its only auxiliary memory, recognizing exactly the context-free languages, including nested structures like palindromes.
Pyramid (geometry)
A pyramid, also called a polygonal pyramid, is a polyhedron with a polygonal base and triangular faces meeting at an apex, with volume one third of base area times height.
Pythagorean theorem
The Pythagorean theorem, also known as Pythagoras's theorem, states that in a right triangle with legs a and b and hypotenuse c, a² + b² = c².
Pythagorean triple
A Pythagorean triple is a set of three positive integers (a, b, c) with a² + b² = c², such as (3, 4, 5), the side lengths of a right triangle.
Q (number format)
Q is a notation for fixed-point binary numbers, devised by Texas Instruments, in which Qm.n names m integer bits and n fractional bits, fixing an implicit scaling factor.
Q-analog
A q-analog, also called a q-analog or q-deformation, is a mathematical expression or identity parameterized by q that reduces to a known classical object when q is set to 1.
Q-Pochhammer symbol
The q-Pochhammer symbol (a;q)n, also called the q-shifted factorial, is the q-analog of the Pochhammer symbol, a finite product that becomes an infinite product building block of q-series and partition generating functions.
q-value (statistics)
John D. Storey introduced the q-value (statistics) in 2002, a measure of significance that defines the minimum false discovery rate at which a test would be called significant.
Q–Q plot
A Q–Q plot (quantile–quantile plot) is a statistical graphic comparing two probability distributions by plotting their quantiles against each other; points off the 45-degree reference line reveal differences in location, scale, or tails.
Q.E.D.
Q.E.D., short for the Latin quod erat demonstrandum ("which was to be demonstrated"), is written at the end of a mathematical proof to signal completion.
QR algorithm
The QR algorithm, or QR method, is an iterative numerical method for computing the eigenvalues of a square matrix, devised by J. G. F. Francis in 1961.
QR decomposition
The QR decomposition, also called QR factorization, expresses a matrix A as A = QR with Q orthogonal and R upper triangular, and underlies least-squares fitting and eigenvalue computation.
Quadratic assignment problem
The quadratic assignment problem (QAP) is a strongly NP-hard combinatorial optimization problem, introduced by Koopmans and Beckmann in 1957, of assigning facilities to locations to minimize total cost.
Quadratic equation
A quadratic equation, also called a second degree equation, is a polynomial equation of degree two, written ax² + bx + c = 0 and solved by the quadratic formula.
Quadratic field
A quadratic field is a number field of degree 2 over the rationals, of the form Q(√d) for a unique squarefree integer d; real when d > 0, imaginary when d < 0.
Quadratic form
A quadratic form is a homogeneous polynomial of degree 2 in several variables, equivalent to a symmetric matrix, and first studied systematically by Gauss in his 1801 Disquisitiones Arithmeticae.
Quadratic formula
The quadratic formula, also called Sridharacharya's formula, is an algebraic formula giving the roots of any quadratic equation directly from its coefficients, derived by completing the square.
Quadratic function
A quadratic function, also called a quadratic trinomial or second-order polynomial, is a polynomial of degree two, written f(x) = ax² + bx + c, whose graph is a parabola.
Quadratic interpolation
Quadratic interpolation is a numerical analysis method that estimates intermediate function values by fitting the unique parabola through three known data points and evaluating it between them.
Quadratic programming
Quadratic programming (QP) optimizes a quadratic objective function subject to linear constraints. Convex QP is solvable reliably and arises in portfolio optimization, support vector machines, and model predictive control.
Quadratic reciprocity
Quadratic reciprocity is a number theory theorem relating the solvability of x² ≡ q (mod p) and x² ≡ p (mod q) for distinct odd primes.