an orthogonal basis are normalized, the resulting basis is an orthonormal basis. Any orthogonal basis can be used to define a system of orthogonal coordinates...

and orthogonal to each other. For example, the standard basis for a Euclidean space R n {\displaystyle \mathbb {R} ^{n}} is an orthonormal basis, where...

a right angle, whereas orthogonal is used in generalizations, such as orthogonal vectors or orthogonal curves. Orthogonality is also used with various...

which the vector space admits a particularly simple kind of basis known as an orthogonal basis (at least when the characteristic of the field is not 2)....

families of functions are used to form an orthogonal basis, such as in the contexts of orthogonal polynomials, orthogonal functions, and combinatorics. In geometry...

notions of "basis" that exist when infinite-dimensional vector spaces are endowed with extra structure. The most important alternatives are orthogonal bases...

In mathematics, the orthogonal group in dimension n, denoted O(n), is the group of distance-preserving transformations of a Euclidean space of dimension...

the method of empirical orthogonal function (EOF) analysis is a decomposition of a signal or data set in terms of orthogonal basis functions which are determined...

powers Orthogonal basis – Basis for v whose vectors are mutually orthogonal Orthogonal complement – Concept in linear algebra Orthonormal basis – Specific...

In mathematics, orthogonal coordinates are defined as a set of d coordinates q = ( q 1 , q 2 , … , q d ) {\displaystyle \mathbf {q} =(q^{1},q^{2},\dots...

step 2, find an orthogonal basis of its eigenspace. Step 4: normalize all eigenvectors in step 3 which then form an orthonormal basis of R {\displaystyle...

In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express...

matrices. When interpreted as the matrices of the action of a set of orthogonal basis vectors for contravariant vectors in Minkowski space, the column vectors...

the goal of lattice basis reduction is to find a basis with short, nearly orthogonal vectors when given an integer lattice basis as input. This is realized...

semidefinite (PSD) matrix yields an orthogonal basis of eigenvectors, each of which has a nonnegative eigenvalue. The orthogonal decomposition of a PSD matrix...

to the kernel, then the projection is an orthogonal projection. When these basis vectors are not orthogonal to the kernel, the projection is an oblique...

may be identified by the label Clp,q(R), indicating that V has an orthogonal basis with p elements with ei2 = +1, q with ei2 = −1, and where R indicates...

geometry, a set K ⊂ Rd is defined to be orthogonally convex if, for every line L that is parallel to one of standard basis vectors, the intersection of K with...

the standard basis (Cartesian) and h or b is for the curvilinear basis. These may not have unit length, and may also not be orthogonal. In the case that...

respect to an orthonormal basis) of an orthogonal transformation is an orthogonal matrix. Its rows are mutually orthogonal vectors with unit norm, so...

function into a sum of square integrable orthogonal basis functions. The standard Fourier series uses an orthonormal basis of trigonometric functions, and the...

{\displaystyle f\neq g} . As with a basis of vectors in a finite-dimensional space, orthogonal functions can form an infinite basis for a function space. Conceptually...

as coordinates. The axes directions represent an orthogonal basis. The combination of origin and basis forms a coordinate frame called the Cartesian frame...

possible answer to this question. The functions en(θ) = e2πinθ form an orthogonal basis of the Hilbert space L2([0, 1]). Consequently, any square-integrable...

mixing angles are the angles between two sets of (complex-valued) orthogonal basis vectors, or states, usually the eigenbases of two quantum mechanical...

, the LLL algorithm calculates an LLL-reduced (short, nearly orthogonal) lattice basis in time O ( d 5 n log 3 ⁡ B ) {\displaystyle {\mathcal {O}}(d^{5}n\log...

function libraries, like in the mathematical concept: an orthogonal function set is easy to use as a basis into expanded functions, ensuring that parts don’t...

e_{1}e_{2}e_{3}\}} A basis formed this way is called a standard basis for the geometric algebra, and any other orthogonal basis for V {\displaystyle V}...

basis) Orthonormal basis in an inner-product space Orthogonal polynomials Fourier analysis and Fourier series Harmonic analysis Orthogonal wavelet Biorthogonal...

In telecommunications, orthogonal frequency-division multiplexing (OFDM) is a type of digital transmission used in digital modulation for encoding digital...