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The Gershgorin circle theorem (where "Gershgorin" is sometimes also spelled "Gersgorin" or "Gerschgorin") identifies a region in the complex plane that contains all the ...

In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points. Singularities ...

The division of two complex numbers can be accomplished by multiplying the numerator and denominator by the complex conjugate of the denominator, for example, with z_1=a+bi ...

Cis(x) is another name for the complex exponential, Cis(x)=e^(ix)=cosx+isinx. (1) It has derivative d/(dz)Cis(z)=ie^(iz) (2) and indefinite integral intCis(z)dz=-ie^(iz). (3)

The roots (sometimes also called "zeros") of an equation f(x)=0 are the values of x for which the equation is satisfied. Roots x which belong to certain sets are usually ...

A measure which takes values in the complex numbers. The set of complex measures on a measure space X forms a vector space. Note that this is not the case for the more common ...

Analytic continuation (sometimes called simply "continuation") provides a way of extending the domain over which a complex function is defined. The most common application is ...

Every complex matrix A can be broken into a Hermitian part A_H=1/2(A+A^(H)) (i.e., A_H is a Hermitian matrix) and an antihermitian part A_(AH)=1/2(A-A^(H)) (i.e., A_(AH) is ...

A Banach limit is a bounded linear functional f on the space ł^infty of complex bounded sequences that satisfies ||f||=f(1)=1 and f({a_(n+1)})=f({a_n}) for all {a_n} in ...

The operator B^~ defined by B^~f(z)=int_D((1-|z|^2)^2)/(|1-zw^_|^4)f(w)dA(w) for z in D, where D is the unit open disk and w^_ is the complex conjugate (Hedenmalm et al. ...