Search results
Results From The WOW.Com Content Network
It is used to solve systems of linear differential equations. In the theory of Lie groups, the matrix exponential gives the exponential map between a matrix Lie algebra and the corresponding Lie group. Let X be an n×n real or complex matrix. The exponential of X, denoted by e X or exp(X), is the n×n matrix given by the power series = =!
The binary number system expresses any number as a sum of powers of 2, and denotes it as a sequence of 0 and 1, separated by a binary point, where 1 indicates a power of 2 that appears in the sum; the exponent is determined by the place of this 1: the nonnegative exponents are the rank of the 1 on the left of the point (starting from 0), and ...
In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas ), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. A tridiagonal system for n unknowns may be written as. where and . For such systems, the solution can be ...
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, it is possible to expand the polynomial (x + y) n into a sum involving terms of the form ax b y c, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending ...
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, 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 ...
t. e. In statistics, linear regression is a statistical model which estimates the linear relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables ). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple ...
Graph of points and linear least squares lines in the simple linear regression numerical example The 0.975 quantile of Student's t -distribution with 13 degrees of freedom is t * 13 = 2.1604 , and thus the 95% confidence intervals for α and β are
Here the ordinary least squares method is used to construct the regression line describing this law. 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 ...