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R Programming, Data Science for Engineers - Coggle Diagram

- - - - TRUE / FALSE
    - - Set of all Integers
    - - Set of all real numbers
    - - Set of all complex numbers
    - - "a", "b", "c",... "#", "%",... "1", "2",...
  - - - Recasting
        
        Method 1
        
        Melt and Cast
        
        Method 2
        
        Recast
      - Joining
- - - - Rows: Samples
      - Columns: Features
    - - Rank of Matrix: Number of Linearly independent attributes/ features
      - R Code: Rank(A)
      - Work with reduced set of variables
      - Dependent variables can be calculated if data is generated from the same data generation process
    - - Null Space / Nullity
      - Every Null Space vector corresponds to one Linear Relationship
    - - Rank + Nullity = attributes
  - - - m = n
        
        A is full rank, |A| != 0
        
        Unique Solution : x = inv(A)b
        
        A is not full rank
        
        Consistent: Infinite Solution
        
        Inconsistent : No Solution
      - m < n
        
        Infinite Solution
        
        However, we can find some appropriate solution from Optimization perspective.
        
        Minimize: trans(Ax-b) (Ax-b)
        
        Ax-b is a vector
        
        Further Details
      - m > n
        
        In general, No solution
  - - - Unit Vector
      - Orthogonal Vectors
      - Orthonormal Vectors
      - Vector Space
        
        Basis Vectors
        
        Linearly independent vectors
        
        Span of basis vectors is vector space
        
        Not unique. can be infinitely many sets of basis vectors for a vector space
        
        for each set of basis, number of vectors is always same.
        
        How to find # of basis vectors of a matrix
        
        Rank of Matrix
        
        Helpful in reducing dataset size, dimensionality reduction, etc.
        
        Subspace
    - - trans(n).X + b = 0
        
        X = Variable Vector
        
        Trans(n) = Normal Vector