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A trace diagram representing the adjugate of a matrix. In mathematics, trace diagrams are a graphical means of performing computations in linear and multilinear algebra. They can be represented as (slightly modified) graphs in which some edges are labeled by matrices. The simplest trace diagrams represent the trace and determinant of a matrix.
A Poincaré plot, named after Henri Poincaré, is a graphical representation used to visualize the relationship between consecutive data points in time series to detect patterns and irregularities in the time series, revealing information about the stability of dynamical systems, providing insights into periodic orbits, chaotic motions, and bifurcations.
In this case, the graph is called an edge-labeled graph. When the edge labels are members of an ordered set (e.g., the real numbers), it may be called a weighted graph. When used without qualification, the term labeled graph generally refers to a vertex-labeled graph with all labels
For =, the only possibility is two points of each nonzero sign, representing a convex quadrilateral. For =, there are two possible Gale diagrams: the diagram with two points of each nonzero sign and one zero point represents a square pyramid, while the diagram with two points of one nonzero sign and three points with the other sign represents ...
The two intersection points are (, +) = (,) and (, +) = (,), and the positions of these intersection points are constant and do not depend on the value of r. An example of a spider web projection of a trajectory on the graph of the logistic map, and the locations of the fixed points x f 1 {\displaystyle x_{f1}} and x f 2 {\displaystyle x_{f2 ...
A chord diagram is a graphical method of displaying the inter-relationships between data in a matrix. The data are arranged radially around a circle with the relationships between the data points typically drawn as arcs connecting the data. The format can be aesthetically pleasing, making it a popular choice in the world of data visualization.
In general, a distance matrix is a weighted adjacency matrix of some graph. In a network, a directed graph with weights assigned to the arcs, the distance between two nodes of the network can be defined as the minimum of the sums of the weights on the shortest paths joining the two nodes (where the number of steps in the path is bounded). [2]
In mathematics, a bilinear map is a function combining elements of two vector spaces to yield an element of a third vector space, and is linear in each of its arguments. Matrix multiplication is an example. A bilinear map can also be defined for modules. For that, see the article pairing.