hermiticity
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Compact operator on Hilbert space — In functional analysis, compact operators on Hilbert spaces are a direct extension of matrices: in the Hilbert spaces, they are precisely the closure of finite rank operators in the uniform operator topology. As such, results from matrix theory… … Wikipedia
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Positive-definite matrix — In linear algebra, a positive definite matrix is a matrix that in many ways is analogous to a positive real number. The notion is closely related to a positive definite symmetric bilinear form (or a sesquilinear form in the complex case). The… … Wikipedia
Spectral theorem — In mathematics, particularly linear algebra and functional analysis, the spectral theorem is any of a number of results about linear operators or about matrices. In broad terms the spectral theorem provides conditions under which an operator or a … Wikipedia
Singular value decomposition — Visualization of the SVD of a 2 dimensional, real shearing matrix M. First, we see the unit disc in blue together with the two canonical unit vectors. We then see the action of M, which distorts the disk to an ellipse. The SVD decomposes M into… … Wikipedia
Matrix mechanics — Quantum mechanics Uncertainty principle … Wikipedia
Gamma matrices — In mathematical physics, the gamma matrices, {γ0,γ1,γ2,γ3}, also known as the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra… … Wikipedia
Choi's theorem on completely positive maps — In mathematics, Choi s theorem on completely positive maps (after Man Duen Choi) is a result that classifies completely positive maps between finite dimensional (matrix) C* algebras. An infinite dimensional algebraic generalization of Choi s… … Wikipedia
Range criterion — In quantum mechanics, in particular quantum information, the Range criterion is a necessary condition that a state must satisfy in order to be separable. In other words, it is a separability criterion . The result Consider a quantum mechanical… … Wikipedia
Theoretical and experimental justification for the Schrödinger equation — The theoretical and experimental justification for the Schrödinger equation motivates the discovery of the Schrödinger equation, the equation that describes the dynamics of nonrelativistic particles. The motivation uses photons, which are… … Wikipedia
