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  2. File:Jim Hefferon - Linear Algebra (4th Edition).pdf - Wikipedia

    en.wikipedia.org/wiki/File:Jim_Hefferon_-_Linear...

    English: Linear Algebra by Jim Hefferon, along with its answers to exercises, is a text for a first undergraduate course. It is Free. Use it as the main book, as a supplement, or for independent study.

  3. Linear algebra - Wikipedia

    en.wikipedia.org/wiki/Linear_algebra

    In three-dimensional Euclidean space, these three planes represent solutions to linear equations, and their intersection represents the set of common solutions: in this case, a unique point. The blue line is the common solution to two of these equations. Linear algebra is the branch of mathematics concerning linear equations such as:

  4. System of equations - Wikipedia

    en.wikipedia.org/wiki/System_of_equations

    In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought. An equation system is usually classified in the same manner as single equations, namely as a: System of linear equations, System of nonlinear equations,

  5. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    Algebra is the art of manipulating equations and formulas. Diophantus (3rd century) and al-Khwarizmi (9th century) were the two main precursors of algebra. [27] [28] Diophantus solved some equations involving unknown natural numbers by deducing new relations until he obtained the solution. [29]

  6. Linear equation - Wikipedia

    en.wikipedia.org/wiki/Linear_equation

    Conversely, every line is the set of all solutions of a linear equation. The phrase "linear equation" takes its origin in this correspondence between lines and equations: a linear equation in two variables is an equation whose solutions form a line. If b ≠ 0, the line is the graph of the function of x that has been defined in the preceding ...

  7. Runge–Kutta methods - Wikipedia

    en.wikipedia.org/wiki/Runge–Kutta_methods

    This can be contrasted with implicit linear multistep methods (the other big family of methods for ODEs): an implicit s-step linear multistep method needs to solve a system of algebraic equations with only m components, so the size of the system does not increase as the number of steps increases.

  8. Ordinary least squares - Wikipedia

    en.wikipedia.org/wiki/Ordinary_least_squares

    In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one [clarification needed] effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values ...

  9. Gröbner basis - Wikipedia

    en.wikipedia.org/wiki/Gröbner_basis

    Gröbner bases are primarily defined for ideals in a polynomial ring = [, …,] over a field K.Although the theory works for any field, most Gröbner basis computations are done either when K is the field of rationals or the integers modulo a prime number.

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