* In the spectral decomposition of matrices, lambda indicates the diagonal matrix of the eigenvalues of the matrix ( mathematics ).

The mathematics of the spectral behavior reveals that there are two regions of particular interest:

This is the spectral theorem in mathematics, and in a finite state space it is just a statement of the completeness of the eigenvectors of a Hermitian matrix.

In mathematics, particularly linear algebra and functional analysis, the spectral theorem is any of a number of results about linear operators or about matrices.

Spectral models generally use a gaussian grid, because of the mathematics of transformation between spectral and grid-point space.

In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces.

In mathematics, spectral graph theory is the study of properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated to the graph, such as its adjacency matrix or Laplacian matrix.

* Joint spectral radius, in mathematics

In mathematics, a spectral space is a topological space which is homeomorphic to the spectrum of a commutative ring.

In mathematics, the Hilbert – Pólya conjecture is a possible approach to the Riemann hypothesis, by means of spectral theory.

In mathematics, spectral theory deals with attempts to understand operators, graphs and dynamical systems by means of the spectrum of eigenvalues associated with the system.

* EHP spectral sequence in mathematics

In mathematics, the Frölicher spectral sequence ( often misspelled as Fröhlicher ) is a tool in the theory of complex manifolds, for expressing the potential failure of the results of cohomology theory that are valid in general only for Kähler manifolds.

) In modern mathematics, this formula can be derived using integral calculus, i. e. disk integration to sum the volumes of an infinite number of circular disks of infinitesimally small thickness stacked centered side by side along the x axis from where the disk has radius r ( i. e. ) to where the disk has radius 0 ( i. e. ).

In mathematics, the radius of convergence of a power series is the radius of the largest disk in which the series converges.

He replaced Ptolemy's chords with the sines from Arabic mathematics, and calculated tables of sines for every minute of arc for a radius of 600, 000 units.

The case when the radius of convergence is 0 yields many interesting series in mathematics, for example the incomplete gamma function has the asymptotic expansion

In mathematics, a Ford circle is a circle with centre at ( p / q, 1 /( 2q < sup > 2 </ sup >)) and radius 1 /( 2q < sup > 2 </ sup >), where p / q is an irreducible fraction, i. e. p and q are coprime integers.

In mathematics, the Hawaiian earring H is the topological space defined by the union of circles in the Euclidean plane R < sup > 2 </ sup > with center ( 1 / n, 0 ) and radius 1 / n for n = 1, 2, 3, ....

The resulting ellipse of distortion will also have infinitesimal radius, but by the mathematics of differentials, the ratios of these infinitesimal values are finite.

In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number.

A classic proof by contradiction from mathematics is the proof that the square root of 2 is irrational.

In mathematics, a square root of a number a is a number y such that y < sup > 2 </ sup > = a, or, in other words, a number y whose square ( the result of multiplying the number by itself, or y × y ) is a.

In mathematics, a square-free, or quadratfrei, integer is one divisible by no perfect square, except 1.

* Quadrature ( mathematics ), drawing a square with the same area as a given plane figure ( squaring ) or computing that area

In recreational mathematics, a magic square of order n is an arrangement of n < sup > 2 </ sup > numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant.

Right: Disk ( mathematics ) | Disk surface, square surface, surface of a hemisphere.

In mathematics, the root mean square ( abbreviated RMS or rms ), also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity.

In mathematics, a complex square matrix U is unitary if

The progression through the First Meditation, leading to the introduction of the concept of the evil genius at the end, is to introduce various categories into the set of dubitables, such as mathematics ( i. e. Descartes ' addition of 2 and 3 and counting the sides of a square ).

In mathematics, and in particular linear algebra, a skew-symmetric ( or antisymmetric or antimetric ) matrix is a square matrix A whose transpose is also its negative ; that is, it satisfies the equation If the entry in the and is a < sub > ij </ sub >, i. e. then the skew symmetric condition is For example, the following matrix is skew-symmetric:

In mathematics, an Hermitian matrix ( or self-adjoint matrix ) is a square matrix with complex entries that is equal to its own conjugate transpose – that is, the element in the i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column, for all indices i and j:

In mathematics, a square number, sometimes also called a perfect square, is an integer that is the square of an integer ; in other words, it is the product of some integer with itself.

In mathematics an automorphic number ( sometimes referred to as a circular number ) is a number whose square " ends " in the same digits as number itself.

In mathematics, in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry 1 in each row and each column and 0s elsewhere.

In mathematics, a unit square is a square whose sides have length 1.

In mathematics, completing the square is considered a basic algebraic operation, and is often applied without remark in any computation involving quadratic polynomials.

In mathematics, specifically functional analysis, Mercer's theorem is a representation of a symmetric positive-definite function on a square as a sum of a convergent sequence of product functions.

In mathematics, the isoperimetric inequality is a geometric inequality involving the square of the circumference of a closed curve in the plane and the area of a plane region it encloses, as well as its various generalizations.

Berkeley sought to take mathematics apart, claimed to uncover numerous gaps in proof, attacked the use of infinitesimals, the diagonal of the unit square, the very existence of numbers, etc.

Other examples are readily found in different areas of mathematics, for example, vector addition, matrix multiplication and conjugation in groups.

* Gramian matrix, used in mathematics to test for linear independence of functions

This value is often calculated as the dominant eigenvalue of the age / size class matrix ( mathematics ).

Heisenberg's matrix mechanics formulation was based on algebras of infinite matrices, a very radical formulation in light of the mathematics of classical physics, although he started from the index-terminology of the experimentalists of that time, not even aware that his " index-schemes " were matrices, as Born soon pointed out to him.

* Symmetric positive-definite matrix, in mathematics

The Julia set of a function ƒ is commonly denoted J ( ƒ ), and the Fatou set is denoted F ( ƒ ).< ref > Note that for other areas of mathematics the notation can also represent the Jacobian matrix of a real valued mapping between smooth manifolds .</ ref > These sets are named after the French mathematicians Gaston Julia and Pierre Fatou whose work began the study of complex dynamics during the early 20th century.

In mathematics, factorization ( also factorisation in British English ) or factoring is the decomposition of an object ( for example, a number, a polynomial, or a matrix ) into a product of other objects, or factors, which when multiplied together give the original.

The column vectors of a matrix ( mathematics ) | matrix.

The n × n orthogonal matrices form a group under matrix multiplication, the orthogonal group denoted by O ( n ), which — with its subgroups — is widely used in mathematics and the physical sciences.

In mathematics, the general linear group of degree n is the set of n × n invertible matrices, together with the operation of ordinary matrix multiplication.

In mathematics, matrix addition is the operation of adding two matrices by adding the corresponding entries together.

In mathematics, matrix multiplication is a binary operation that takes a pair of matrices, and produces another matrix.

In mathematics, the special linear group of degree n over a field F is the set of n × n matrices with determinant 1, with the group operations of ordinary matrix multiplication and matrix inversion.

In mathematics, the unitary group of degree n, denoted U ( n ), is the group of n × n unitary matrices, with the group operation that of matrix multiplication.

In mathematics, on a finite-dimensional inner product space, a self-adjoint operator is an operator that is its own adjoint, or, equivalently, one whose matrix is Hermitian, where a Hermitian matrix is one which is equal to its own conjugate transpose.