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  2. Argument (complex analysis) - Wikipedia

    en.wikipedia.org/wiki/Argument_(complex_analysis)

    Figure 1. This Argand diagram represents the complex number lying on a plane.For each point on the plane, arg is the function which returns the angle . In mathematics (particularly in complex analysis), the argument of a complex number z, denoted arg(z), is the angle between the positive real axis and the line joining the origin and z, represented as a point in the complex plane, shown as in ...

  3. Positive and negative parts - Wikipedia

    en.wikipedia.org/wiki/Positive_and_negative_parts

    The converse, though, does not necessarily hold: for example, taking f as =, where V is a Vitali set, it is clear that f is not measurable, but its absolute value is, being a constant function. The positive part and negative part of a function are used to define the Lebesgue integral for a real-valued function.

  4. Positive-definite function - Wikipedia

    en.wikipedia.org/wiki/Positive-definite_function

    Positive-definiteness arises naturally in the theory of the Fourier transform; it can be seen directly that to be positive-definite it is sufficient for f to be the Fourier transform of a function g on the real line with g(y) ≥ 0.

  5. Complex number - Wikipedia

    en.wikipedia.org/wiki/Complex_number

    The study of functions of a complex variable is known as complex analysis and has enormous practical use in applied mathematics as well as in other branches of mathematics. Often, the most natural proofs for statements in real analysis or even number theory employ techniques from complex analysis (see prime number theorem for an example).

  6. Definite matrix - Wikipedia

    en.wikipedia.org/wiki/Definite_matrix

    In mathematics, a symmetric matrix with real entries is positive-definite if the real number is positive for every nonzero real column vector, where is the row vector transpose of . [1] More generally, a Hermitian matrix (that is, a complex matrix equal to its conjugate transpose) is positive-definite if the real number is positive for every nonzero complex column vector , where denotes the ...

  7. QRS complex - Wikipedia

    en.wikipedia.org/wiki/QRS_complex

    Diagram showing how the polarity of the QRS complex in leads I, II, and III can be used to estimate the heart's electrical axis in the frontal plane. The QRS complex is the combination of three of the graphical deflections seen on a typical electrocardiogram (ECG or EKG). It is usually the central and most visually obvious part of the tracing.

  8. Complex analysis - Wikipedia

    en.wikipedia.org/wiki/Complex_analysis

    A complex function is a function from complex numbers to complex numbers. In other words, it is a function that has a (not necessarily proper) subset of the complex numbers as a domain and the complex numbers as a codomain. Complex functions are generally assumed to have a domain that contains a nonempty open subset of the complex plane.

  9. Polylogarithm - Wikipedia

    en.wikipedia.org/wiki/Polylogarithm

    In mathematics, the polylogarithm (also known as Jonquière's function, for Alfred Jonquière) is a special function Li s (z) of order s and argument z. Only for special values of s does the polylogarithm reduce to an elementary function such as the natural logarithm or a rational function .