Maths for Machine Learning

Hello Readers,

I am re-starting my blogging today from a long break and this time I going to start with some interesting topics of mathematics which is going to helpful for Machine Learning or Data science, we also use Jupyter notebook to demonstrate the maths calculations with python.

For today we are going to have a look at scalar, vector, matrices and tensor.
  1. What is scalar?
    • Scalar is a single real number or value can be considered as scalar.
    • Any real number or value that able to show any information is scalar.
      • ex: temperature, weight, length etc.
    • For computer programing you can consider a numeric variable as a scalar.
      • i.e : int number1=10;
    • A scalar have only magnitude (size/quantity) but no direction.

  2. What is Vector?
    • Vector is an array of numbers, either in a row or in a column, which can be identified by index.
    • For computer programing we can consider an array or list or set as vector.
      • Integer numbers[] = new Integer[10];
      • List<Integers> listOfNumbers = new ArrayList<Integers>;
    • A Vector has two properties,
      • Magnitude : size / quantity
      • Direction : Direction of vector from one place to another.

  3. What is Matrices?
    • Matrices is a way to organize data into rows and columns.
    • It is 2D array of numbers, where each element can be identified by two indices.
    • For computer programming we can consider 2D array.
      • Integer matrices[2][2] = new Integer[2][2];
    • Each item/data in matrices is called as element or entry.
    • Matrix has 2-axis on graph diagram.

  4. What is tensor?
    • Tensor is an array of numbers with more than 2D space.
    • Matrix has 2-axes, where tensor can be represented in more than 2-axes.
    • In a simple term it's array of numbers with variable number of axes.
    • if 2D (Matix) has indices (i,j) then 3D has indices (i,j,k)

Scalar, vector and Matrices:



Tensors:



References : 
  1. http://www.mathwords.com/
  2. https://www.mathwarehouse.com/
  3. https://stattrek.com/matrix-algebra/
  4. https://www.khanacademy.org/math/algebra-home/alg-matrices
  5. https://www.youtube.com/watch?v=f5liqUk0ZTw

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