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Machine Learning From scratch | Part 3. Matrices and matrices Dot Product

Prerequisit : Vector Dot Products

Matrices are grid of numbers or arrangment of numbers . In programming it can be an array of array

a real example can be marks of students (A,B,C) in subjects (S1,S2,S3)

can be shown as Student

A have scored 20 in S1 , 25 in S2 and 30 in S3 = [20,25,30]

B have scored 25 in S1 , 15 in S2 and 20 in S3 = [25,15,20]

C have scored 35 in S1 , 25 in S2 and 30 in S3 = [35,25,30]

S1    S2    S3     ----> Row

A 20 25 30

B 25 15 20

C 35 25 30
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V
Columns

Matrix Shape

Every matrix has a shape which is

number of rows * number of columns 

for our above matrix we can say it is a 3*3 matrix as it has 3 rows and 3 columns

Matrix Dot Products

we have one matrix A of shape 2*3 (which means we have 2 row and 3 column ) and we have one more matrix B of shape 3*2 (which means we have 3 rows and 2 column )

for matrix multiplications thier is one rule which should be statisfied
A(2*3) B(3*2) the number of columns of first matrix and number of rows in second matrix showld be equal

in First matrix no columns is 3
in Second matrix no rows is 3

the result will be a matrix of shape numer of rows from first matrix * number of columns in second matrix for our example

result = matrix of shape 2*2 (2 rows and 2 columns)


wo we can multiply this two matrices

A = a1 a2 a3 B = b1 b2
a4 a5 a6 b3 b4
b5 b6

AB = a1b1 + a2b3 + a3b5 a1b2 + a2b4 + a3b6
a4b1 + a5b3 + a6b5 a4b2 + a5b4 + a6b6


Lets See by Example


A = [[1,2,3],[4,5,6]]
B = [[1,2],[3,5],[4,2]] --> this has 3 rows and 2 column


A = 1 2 3 B = 1 2
4 5 6 3 5
4 2
AB = 1*1 + 2*3 + 3*4 1*2 + 2*5 + 3*2
4*1 + 5*3 + 6*4 4*2 + 5*5 + 6*2

= 1+6+12 2+10+6
4+15+24 8+25+12

= 19 18
43 45

In the next article we will see how to calculate it in program

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Neeraj Dana

Neeraj Dana

Experienced Software Engineer with a demonstrated history of working in the information technology and services industry. Skilled in Angular,React,React-Native,