mekhiya/ai-math

Statistics, Linear Algebra, Probability, and Calculus. Mathematical Concepts . Statistics core part of models. Calculus to learn & optimize a model.

ai-math

Statistics, Linear Algebra, Probability, and Calculus. Mathematical Concepts . Statistics core part of models. Calculus to learn & optimize a model.

Multivariable Calculus

Single variable function: f(x) = x² , whereas multi-variable function: f(x,y) = x² + y. (point on xy graph) (x-y point to a number) [also called single variable calculus]

In multivariable o/p can vector: f(x,y) = [ 3x / 2y ] (x-y point gives vector result - point to a vector [result as vector or matrix]

x-y point as input to function gives graph as result - example :

Dot product & Cross product

1. dot product returns a number but cross product returns vector
2. dot product works in any number of dimensions, cross porduct works only in 3d
3. dot product measures how much two vector point in same direction. cross product measures how much two vectors point in different direction.

Matrix

Matrix Transpose

Vector as matrices

vector is just a list of numbers. We can write vector as matrices in either (1 x n) format or (n x 1) format

vedtor can be written a 1 x n - one row and n column - example - 1x 3 - [1,4,5] (one row, n column). ABove transposed to n x 1 (n row, 1 column)

Interactive version - i j define plane. Vector gets multiplied on this place

Point in 3D

f(x,y) = x² + y²

f(x,y) = 1/4 x² + 1/4 y²

Contour Plots | Multivariable calculus