Linear Algebra - Linear Equation
About
A linear equation represents a linear function that forms a straight line.
A common form of a linear equation in the two variables (two dimensions) x and y is
<math>
y= mx + b
</math>
where:
-
b is a constant named the
intercept. It determines the point at which the line crosses the y-axis, otherwise known as the y-intercept.
In Statistics, it's the basic of a regression
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Assumptions
Terms of linear equations cannot contain:
products of distinct or equal variables,
nor any power (other than 1)
or other function of a variable, equations involving terms such as xy, x2, y1/3, and sin(x)
Linear Equation in
Vector
In linear algebra, a linear equation can be expressed as an equation stating the value of the dot-product of:
Therefore a linear equation (function) is an equation of the form
<math>a . x = \beta</math>
where:
a is a coefficient
vector (for instance <math> 1, 4, -3, \dots, 2</math>
),
x is a vector of unknowns variables (for instance <math> x, y, z</math>
or <math> x_1, \dots, x_n</math>
)
and <math>\beta</math>
is a
scalar (for instance, 3)
Type
Homogeneous
A linear equation a · x = 0 with zero right-hand side is a homogeneous linear equation.
A system of homogeneous linear equations is called a homogeneous linear system.
Functions
Oracle:
Documentation / Preference