Artificial Intelligence

Linear Algebra

An AI expert cannot live without Linear Algebra:

  • Linear algebra is a branch of Mathematics
  • Linear algebra plays an important role in Statistics
  • Linear algebra represents the Math of Data

Linear Graphic

Linear means straight. A Linear Graph is a Straight Line.

In general, a linear graph displays a Linear Function.

A Function is special relationship where each input has an output.

A function is often written as f(x) where x is the input value:

xyy = x
11when x = 1, y = 1
22when x = 2, y = 2
33when x = 3, y = 3
44when x = 4, y = 4
55when x = 5, y = 5

Results from f(x) = 2x

xyy = 2x
12when x = 1, y = 2
24when x = 2, y = 4
36when x = 3, y = 6
48when x = 4, y = 8
510when x = 5, y = 10

Linear Algebra is the branch of mathematics thast concers linear equations (and linear maps) and their representations in vector spaces and through matrices.

Linear algebra is central to almost all areas of mathematics.


Linear Equations

A Linear Equation is an equation for a straight line:

  • y = x
  • y = x*2
  • y = x*2 + 7
  • y = ax + b
  • 5x = 3y
  • y/2 = 6

A Linear Equation can NOT contain exponents or square roots:

  • y = x**2
  • y = Math.sqrt(x)
  • y = Math.sin(x)

Linear Regression

A Linear regression tries to model the relationship between two variables by fitting a linear graph to data.

One variable (x) is considered to be data, and the other (y) is considered to be dependent.

For example, a Linear Regression can be a model to relate the price of houses to their size.

Linear Least Squares

Linear algebra is used to solve Linear Equations.

Linear Least Squares (LLS) is a set of formulations for solving statistical problems involved in Linear Regression.

Matrix Factorization

With AI, you need to know how to factorize a matrix.

Matrix factorization is a key tool in linear algebra, especially in Linear Least Squares.