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2. Singularity (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Singularity_(mathematics)

   Singularity (mathematics) In mathematics, a singularity is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as by lacking differentiability or analyticity. [1][2][3] For example, the reciprocal function has a singularity at , where the ...

3. Singularity theory - Wikipedia

   en.wikipedia.org/wiki/Singularity_theory

   Singularity theory. In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it on the floor, and flattening it. In some places the flat string will cross itself ...

4. Singular value decomposition - Wikipedia

   en.wikipedia.org/wiki/Singular_value_decomposition

   Bottom: The action of Σ, a scaling by the singular values σ1 horizontally and σ2 vertically. Right: The action of U, another rotation. In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix into a rotation, followed by a rescaling followed by another rotation.

5. Milnor number - Wikipedia

   en.wikipedia.org/wiki/Milnor_number

   Milnor number. In mathematics, and particularly singularity theory, the Milnor number, named after John Milnor, is an invariant of a function germ. If f is a complex-valued holomorphic function germ then the Milnor number of f, denoted μ (f), is either a nonnegative integer, or is infinite. It can be considered both a geometric invariant and ...

6. Resolution of singularities - Wikipedia

   en.wikipedia.org/wiki/Resolution_of_singularities

   Blowing up. Repeatedly blowing up the singular points of a curve will eventually resolve the singularities. The main task with this method is to find a way to measure the complexity of a singularity and to show that blowing up improves this measure. There are many ways to do this.

7. Singular point of an algebraic variety - Wikipedia

   en.wikipedia.org/wiki/Singular_point_of_an...

   Singular point of an algebraic variety. In the mathematical field of algebraic geometry, a singular point of an algebraic variety V is a point P that is 'special' (so, singular), in the geometric sense that at this point the tangent space at the variety may not be regularly defined. In case of varieties defined over the reals, this notion ...

8. Regular singular point - Wikipedia

   en.wikipedia.org/wiki/Regular_singular_point

   Point a is an ordinary point when functions p1(x) and p0(x) are analytic at x = a. Point a is a regular singular point if p1(x) has a pole up to order 1 at x = a and p0 has a pole of order up to 2 at x = a. Otherwise point a is an irregular singular point. We can check whether there is an irregular singular point at infinity by using the ...

9. Zeros and poles - Wikipedia

   en.wikipedia.org/wiki/Zeros_and_poles

   t. e. In complex analysis (a branch of mathematics), a pole is a certain type of singularity of a complex-valued function of a complex variable. It is the simplest type of non- removable singularity of such a function (see essential singularity). Technically, a point z0 is a pole of a function f if it is a zero of the function 1/f and 1/f is ...