Argand diagram A
complex number can be visually represented as a pair of numbers forming a vector on a diagram called an
Argand diagram. The
complex plane is sometimes called the
Argand plane because it is used in
Argand diagrams. These are named after
Jean-Robert Argand (1768–1822), although they were first described by Norwegian-Danish land surveyor and mathematician
Caspar Wessel (1745–1818). Argand diagrams are frequently used to plot the positions of the
poles and
zeroes of a
function in the complex plane. The concept of the complex plane allows a
geometric interpretation of complex numbers. Under
addition, they add like
vectors. The
multiplication of two complex numbers can be expressed most easily in
polar coordinates — the magnitude or
modulus of the product is the product of the two
absolute values, or moduli, and the angle or
argument of the product is the sum of the two angles, or arguments. In particular, multiplication by a complex number of modulus 1 acts as a rotation.
Butterfly diagram In the context of
fast Fourier transform algorithms, a
butterfly is a portion of the computation that combines the results of smaller
discrete Fourier transforms (DFTs) into a larger DFT, or vice versa (breaking a larger DFT up into subtransforms). The name "butterfly" comes from the shape of the data-flow diagram in the radix-2 case, as described below. The same structure can also be found in the
Viterbi algorithm, used for finding the most likely sequence of hidden states. The
butterfly diagram show a data-flow diagram connecting the inputs
x (left) to the outputs
y that depend on them (right) for a "butterfly" step of a radix-2
Cooley–Tukey FFT algorithm. This diagram resembles a
butterfly as in the
Morpho butterfly shown for comparison, hence the name.
Commutative diagram In mathematics, and especially in
category theory, a commutative diagram is a diagram of
objects, also known as vertices, and
morphisms, also known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition. Commutative diagrams play the role in category theory that equations play in algebra.
Hasse diagrams A
Hasse diagram is a simple picture of a finite
partially ordered set, forming a
drawing of the partial order's
transitive reduction. Concretely, one represents each element of the set as a vertex on the page and draws a line segment or curve that goes upward from
x to
y precisely when
x \lambda (lambda) of a positive integer
n, the total number of boxes of the diagram. The Young diagram is said to be of shape \lambda, and it carries the same information as that partition. Listing the number of boxes in each column gives another partition, the
conjugate or
transpose partition of \lambda; one obtains a Young diagram of that shape by reflecting the original diagram along its main diagonal. Young tableaux were introduced by
Alfred Young, a
mathematician at
Cambridge University, in 1900. They were then applied to the study of symmetric group by
Georg Frobenius in 1903. Their theory was further developed by many mathematicians.
Other mathematical diagrams •
Cremona diagram •
De Finetti diagram •
Dynkin diagram •
Elementary diagram •
Euler diagram •
Stellation diagram •
Ulam spiral •
Van Kampen diagram •
Taylor diagram == See also ==