Addition, multiplication and transpose of lists in python.

Addition of matrices:-

Take the size of the matrix as user input, accept the two matrices and print the resultant matrix after adding the original two matrices.

row=int(input("enter the row"))
column=int(input("enter the column"))
a=[]
b=[]
print("1st matrix elements")
for i in range(0,row):
 a1=[]
 for j in range(0,column):
  e=int(input())
  a1.append(e)
 a.append(a1)
print("2nd matrix elements")
for i in range(0,row):
 b1=[]
 for j in range(0,column):
  e1=int(input())
  b1.append(e1)
 b.append(b1)
c=[]
for i in range(0,row):
 c1=[]
 for j in range(0,column):
  c1.append(0)
 c.append(c1)
for i in range(0,row):
 for j in range(0,column):
  c[i][j]=a[i][j]+b[i][j]
print(c)

Output:-

We have taken inputs the row and column number , accepted the values of two lists. Then we made a zeros matrix c[] of the accepted order, and within loop , we changed the value of c[i][j] to the addition of a[i][j] and b[i][j] .

Multiplication of matrices:-

row=int(input("enter the row matrix1"))
column=int(input("enter the column matrix1"))
row1=int(input("enter the row matrix2"))
column1=int(input("enter the column matrix2"))
a=[]
b=[]
print("1st matrix elements")
for i in range(0,row):
 a1=[]
 for j in range(0,column):
  e=int(input())
  a1.append(e)
 a.append(a1)
print("2nd matrix elements")
for i in range(0,row1):
 b1=[]
 for j in range(0,column1):
  e1=int(input())
  b1.append(e1)
 b.append(b1)
c=[]
for i in range(0,row):
 c1=[]
 for j in range(0,column1):
  c1.append(0)
 c.append(c1)
for i in range(0,row):
 for j in range(0,column1):
  for k in range(0,column):
   c[i][j]+=a[i][k]*b[k][j]
print(c)

Output:-

Rule of matrix multiplication says that, two matrices A_ik and B_mj are only multiplicable if k=m and the resultant matrix will of the order C_ij.

So row and column of resultant matrix is row of first matrix and column of second matrix. And also notation for multiplication is summation of A_ik*B_kj ,where k is the column of the first matrix or row of the second matrix.

Transpose of a matrix:-

Example of a transpose of a matrix is

A=[[1,2,3],[4,5,6],[7,8,9]]

transpose of A=A^T

A^T=[[1,4,7],[2,5,8],[3,6,9]] , so we can see rows are converted to columns and vice versa. So the notation is A^T_ij=A_ji

row=int(input("enter row"))
column=int(input("enter column"))
a=[]
print("matrix elements")
for i in range(0,row):
 a1=[]
 for j in range(0,column):
  e=int(input())
  a1.append(e)
 a.append(a1)
print("original matrix",a)
c=[]
for i in range(0,row):
 c1=[]
 for j in range(0,column):
  c1.append(0)
 c.append(c1)
for i in range(0,row):
 for j in range(0,column):
  c[i][j]=a[j][i]
print("transposed matrix",c)

Output