Day #15 - Data Science - Maths Basics

Day #15 - Mathematics Basics

Sets Basics

• Cardinality - Number of distinct elements in Set (For a Finite Set)
• For Real numbers cardinality infinite

Rational Numbers - Made of Ratio of two numbers
Fibonacci series was introduced in 1201 - Amazing :)

Functions

• Represents relationship between mathematical variables
• Spread of all possible output is called range
• Function that maps from A to B. A is referred as (Domain), B is referred as co-domain

Matrix

• Rows and columns define matrix 
• 2D array of numbers 
• Eigen Values - Scalars, Eigen Vector - Vectors special set of values associated with Matrix M
• Eigen Vectors - Those directions remain unchanged by action of matrix M
• Trace - Sum of diagonal elements
• Rank of Matrix - Number of linearly independent vectors

Determinant

• Can be computed only for square matrix

Vector

• Vectors have magnitude, length and direction
•  Magnitude and cost of angle will give you direction
• Vector product non-commutative
•  Dot product commutative
•  Vector is linearly independent if none of vectors can be written as sum of multiple of other vectors

 Happy Learning!!!