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34 relations: Complex number, Conjugate transpose, Dagger, Dagger (typography), Determinant, Diagonalizable matrix, Eigenvalues and eigenvectors, Group (mathematics), Hermitian adjoint, Hermitian matrix, Identity matrix, Inner product space, Integer, Invertible matrix, Isometry, Mathematics, Matrix (mathematics), Matrix decomposition, Matrix exponential, Matrix similarity, Norm (mathematics), Normal matrix, Orthogonal group, Orthogonal matrix, Orthonormal basis, Probability amplitude, Quantum logic gate, Real number, Special unitary group, Spectral theorem, Symplectic matrix, Unit circle, Unitary group, Unitary operator.
Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Conjugate transpose
In mathematics, the conjugate transpose or Hermitian transpose of an m-by-n matrix A with complex entries is the n-by-m matrix A∗ obtained from A by taking the transpose and then taking the complex conjugate of each entry.
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Dagger
A dagger is a knife with a very sharp point and one or two sharp edges, typically designed or capable of being used as a thrusting or stabbing weapon.
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Dagger (typography)
A dagger, obelisk, or obelus is a typographical symbol usually used to indicate a footnote if an asterisk has already been used.
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Determinant
In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.
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Diagonalizable matrix
In linear algebra, a square matrix A is called diagonalizable if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix P such that P−1AP is a diagonal matrix.
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Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
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Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
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Hermitian adjoint
In mathematics, specifically in functional analysis, each bounded linear operator on a complex Hilbert space has a corresponding adjoint operator.
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Hermitian matrix
In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the -th row and -th column is equal to the complex conjugate of the element in the -th row and -th column, for all indices and: Hermitian matrices can be understood as the complex extension of real symmetric matrices.
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Identity matrix
In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.
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Inner product space
In linear algebra, an inner product space is a vector space with an additional structure called an inner product.
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Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
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Invertible matrix
In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.
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Isometry
In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Matrix (mathematics)
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
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Matrix decomposition
In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices.
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Matrix exponential
In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function.
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Matrix similarity
In linear algebra, two n-by-n matrices and are called similar if for some invertible n-by-n matrix.
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Norm (mathematics)
In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.
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Normal matrix
In mathematics, a complex square matrix is normal if where is the conjugate transpose of.
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Orthogonal group
In mathematics, the orthogonal group in dimension, denoted, is the group of distance-preserving transformations of a Euclidean space of dimension that preserve a fixed point, where the group operation is given by composing transformations.
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Orthogonal matrix
In linear algebra, an orthogonal matrix is a square matrix whose columns and rows are orthogonal unit vectors (i.e., orthonormal vectors), i.e. where I is the identity matrix.
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Orthonormal basis
In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for V whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other.
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Probability amplitude
In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems.
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Quantum logic gate
In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit operating on a small number of qubits.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Special unitary group
In mathematics, the special unitary group of degree, denoted, is the Lie group of unitary matrices with determinant 1.
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Spectral theorem
In mathematics, particularly linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented as a diagonal matrix in some basis).
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Symplectic matrix
In mathematics, a symplectic matrix is a 2n×2n matrix M with real entries that satisfies the condition where MT denotes the transpose of M and Ω is a fixed 2n×2n nonsingular, skew-symmetric matrix.
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Unit circle
In mathematics, a unit circle is a circle with a radius of one.
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Unitary group
In mathematics, the unitary group of degree n, denoted U(n), is the group of unitary matrices, with the group operation of matrix multiplication.
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Unitary operator
In functional analysis, a branch of mathematics, a unitary operator is a surjective bounded operator on a Hilbert space preserving the inner product.
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References
[1] https://en.wikipedia.org/wiki/Unitary_matrix
