Search results
Results From The WOW.Com Content Network
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, is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously ...
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 section.
Generalized Wrońskians. For n functions of several variables, a generalized Wronskian is a determinant of an n by n matrix with entries Di(fj) (with 0 ≤ i < n), where each Di is some constant coefficient linear partial differential operator of order i. If the functions are linearly dependent then all generalized Wronskians vanish.
Some sink, source or node are equilibrium points. 2-dimensional case refers to Phase plane. In mathematics, an autonomous system or autonomous differential equation is a system of ordinary differential equations which does not explicitly depend on the independent variable. When the variable is time, they are also called time-invariant systems.
In vector calculus, the Jacobian matrix (/ dʒəˈkoʊbiən /, [1][2][3] / dʒɪ -, jɪ -/) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. When this matrix is square, that is, when the function takes the same number of variables as input as the number of vector components of its output ...
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3][4]
In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality: [1] < less than > greater than; ≤ less than or equal to; ≥ greater than or equal to; ≠ not equal to; A linear inequality looks exactly like a linear equation, with the inequality sign ...
In multilinear algebra, one considers multivariable linear transformations, that is, mappings that are linear in each of a number of different variables. This line of inquiry naturally leads to the idea of the dual space , the vector space V* consisting of linear maps f : V → F where F is the field of scalars.