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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 ...
A flow graph is a form of digraph associated with a set of linear algebraic or differential equations: [1] [2] "A signal flow graph is a network of nodes (or points) interconnected by directed branches, representing a set of linear algebraic equations. The nodes in a flow graph are used to represent the variables, or parameters, and the ...
In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Power functions – relationships of the form y = a x k {\displaystyle y=ax^{k}} – appear as straight lines in a log–log graph, with the exponent corresponding to ...
MGF is an alternate method to finding the transfer function algebraically by labeling each signal, writing down the equation for how that signal depends on other signals, and then solving the multiple equations for the output signal in terms of the input signal. MGF provides a step by step method to obtain the transfer function from a SFG.
For some authors, a linear signal-flow graph is more constrained than a block diagram, [35] in that the SFG rigorously describes linear algebraic equations represented by a directed graph. For other authors, linear block diagrams and linear signal-flow graphs are equivalent ways of depicting a system, and either can be used to solve the gain. [36]
The linear–log type of a semi-log graph, defined by a logarithmic scale on the x axis, and a linear scale on the y axis. Plotted lines are: y = 10 x (red), y = x (green), y = log(x) (blue). In science and engineering, a semi-log plot/graph or semi-logarithmic plot/graph has one axis on a logarithmic scale, the other on a linear scale.
A linear function is a polynomial function in which the variable x has degree at most one: [2] = +. Such a function is called linear because its graph, the set of all points (, ()) in the Cartesian plane, is a line. The coefficient a is called the slope of the function and of the line (see below).
The special case where all the polynomials are of degree one is called a system of linear equations, for which another range of different solution methods exist, including the classical Gaussian elimination. A polynomial equation for which one is interested only in the solutions which are integers is called a Diophantine equation. Solving ...
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