# singular

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**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… …82

**Singular homology**— In algebraic topology, a branch of mathematics, singular homology refers to the study of a certain set of topological invariants of a topological space X , the so called homology groups H n(X). Singular homology is a particular example of a… …83

**Singular point of an algebraic variety**— In mathematics, a singular point of an algebraic variety V is a point P that is special (so, singular), in the geometric sense that V is not locally flat there. In the case of an algebraic curve, a plane curve that has a double point, such as the …84

**Singular submodule**— In the branches of abstract algebra known as ring theory and module theory, each right (resp. left) R module M has a singular submodule consisting of elements whose annihilators are essential right (resp. left) ideals in R. In set notation it is… …85

**Singular cardinals hypothesis**— In set theory, the singular cardinals hypothesis (SCH) arose from the question of whether the least cardinal number for which the generalized continuum hypothesis (GCH) might fail could be a singular cardinal.According to Mitchell (1992), the… …86

**Singular point of a curve**— In geometry, a singular point on a curve is one where the curve is not given by a smooth embedding of a parameter. The precise definition of a singular point depends on the type of curve being studied. Contents 1 Algebraic curves in the plane 1.1 …87

**Singular and plural**— ◊ GRAMMAR The singular is the form of a count noun or a verb which you use when referring to one person or thing. The plural is the form which you use when referring to more than one person or thing. For details of these forms, see entries at… …88

**singular and plural**— ◊ GRAMMAR The singular is the form of a count noun or a verb which you use when referring to one person or thing. The plural is the form which you use when referring to more than one person or thing. For details of these forms, see entries at… …89

**Singular value**— In mathematics, in particular functional analysis, the singular values, or s numbers of a compact operator T acting on a Hilbert space are defined as the eigenvalues of the operator sqrt{T^*T} (where T * denotes the adjoint of T and the square… …90

**Singular measure**— In mathematics, two positive (or signed or complex) measures μ and ν defined on a measurable space (Ω, Σ) are called singular if there exist two disjoint sets A and B in Σ whose union is Ω such that μ is zero on all measurable subsets of B while… …