Concepts inThe exact analysis of sparse rectangular linear systems
Linear system
A linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that are much simpler than the general, nonlinear case. As a mathematical abstraction or idealization, linear systems find important applications in automatic control theory, signal processing, and telecommunications. For example, the propagation medium for wireless communication systems can often be modeled by linear systems.
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Mathematical analysis, which mathematicians refer to simply as analysis, is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions. These theories are often studied in the context of real numbers, complex numbers, and real and complex functions. Analysis may be conventionally distinguished from geometry.
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Rectangle
In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. Another name is equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°). It can also be defined as a parallelogram containing a right angle. The term oblong is occasionally used to refer to a non-square rectangle. A rectangle with vertices ABCD would be denoted as 10px¿.
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Sparse matrix
In the subfield of numerical analysis, a sparse matrix is a matrix populated primarily with zeros. The term itself was coined by Harry M. Markowitz. Conceptually, sparsity corresponds to systems which are loosely coupled. Consider a line of balls connected by springs from one to the next; this is a sparse system. By contrast, if the same line of balls had springs connecting each ball to all other balls, the system would be represented by a dense matrix.
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