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  2. System of linear equations - Wikipedia

    en.wikipedia.org/wiki/System_of_linear_equations

    A linear system in three variables determines a collection of planes. The intersection point is the solution. In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. [1] [2] For example,

  3. Indeterminate system - Wikipedia

    en.wikipedia.org/wiki/Indeterminate_system

    In linear systems, indeterminacy occurs if and only if the number of independent equations (the rank of the augmented matrix of the system) is less than the number of unknowns and is the same as the rank of the coefficient matrix. For if there are at least as many independent equations as unknowns, that will eliminate any stretches of overlap ...

  4. Linear algebra - Wikipedia

    en.wikipedia.org/wiki/Linear_algebra

    With respect to general linear maps, linear endomorphisms and square matrices have some specific properties that make their study an important part of linear algebra, which is used in many parts of mathematics, including geometric transformations, coordinate changes, quadratic forms, and many other part of mathematics.

  5. Mathematical analysis - Wikipedia

    en.wikipedia.org/wiki/Mathematical_analysis

    Ordinary differential equations appear in celestial mechanics (planets, stars and galaxies); numerical linear algebra is important for data analysis; stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology.

  6. Gauss–Seidel method - Wikipedia

    en.wikipedia.org/wiki/Gauss–Seidel_method

    In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel .

  7. Positional notation - Wikipedia

    en.wikipedia.org/wiki/Positional_notation

    A remnant of this system may be seen in the modern word for 40, daoichead. The Welsh language continues to use a base-20 counting system, particularly for the age of people, dates and in common phrases. 15 is also important, with 16–19 being "one on 15", "two on 15" etc. 18 is normally "two nines". A decimal system is commonly used.

  8. Indeterminate equation - Wikipedia

    en.wikipedia.org/wiki/Indeterminate_equation

    In mathematics, particularly in algebra, an indeterminate equation is an equation for which there is more than one solution. [1] For example, the equation a x + b y = c {\displaystyle ax+by=c} is a simple indeterminate equation, as is x 2 = 1 {\displaystyle x^{2}=1} .

  9. Linear system - Wikipedia

    en.wikipedia.org/wiki/Linear_system

    In other words, if the input x(t) to a linear system is = where δ(t) represents the Dirac delta function, and the corresponding response y(t) of the system is (=) = (,) then the function h(t 2, t 1) is the time-varying impulse response of the system.