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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**Generalizations of Pauli matrices**— In mathematics and physics, in particular quantum information, the term generalized Pauli matrices refers to families of matrices which generalize the (linear algebraic) properties of the Pauli matrices. In this article we give a few classes of… … Wikipedia**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