Basic-Math-For-DS
August 22, 2021
DSML : Basic Math for Datascience
Linear Algebra
- Vectors and Scalars
- Scalar : they are just values that represent something.
- Vector : list of numbers in tabular form that represent something.
- Operations
- Vector addition : Dot product, which is the total work achieved or the displacement in qunatified form.
- Scalar multiplication : when vector multiplied with constant, it either grows or reduces.
- Project : P(V1/V2) proecting V1 over V2 is the shadow of the vector placed on the other. It helps to analyze feature of unknown vector.
- Matrices
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They are just compostion of numbers of expression, where we convert them to Arrays and perform operation. Some computer graphics applications such as Scaling, Rotation, Shearing.
- You can see below, how we converted an equation to a array form.
- Operations
- Addition / Subtraction : Add the matrix of the same order (rows and cols).
- Multiplication : can multiply if the cols of 1st Mat and rows of 2nd Mat match. Means 23 & 32 will result in 2 * 2 Mat.
- Transpose : interchanging of rows and cols, helps you to change the dimension.
- Determinant : is a scalar value, that helps you in knowing the sensitivity or depth of the data. It gives you the product of Eigen values of matrix.
- As seen below, we can see Sx Sy as the scaling factor. M - shearing factor and rotation matrix.
- Solving methods
- Row Echelon Method : it uses Gaussian elimination to solve linear equation. Helps you identify some matrix properties such as Rank, Kernel, Inverse Matrix. Check this link
- Inverse Method : Another way to find the solution of the linear equation. To solve using inverse check this link. Watch video on how to solve equation to know more. A. A-1 = I (identity matrix) A.X = C A-1 A . X = A-1 . C X = A-1C
- Eigen Vectors
- They dont change the direction or the state when the transformation is appliied.
- Most sensitive part of the dataset, which can be used for analysis purpose.
- As shown below, the vector V2 increased in same direction, but did change as V1.
- Applicatons :
- to understand PCA check statquest video
Multivariate calculus
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- Notes