from numpy import arrayA =array([[1, 2, 3], [4, 5, 6]])B =array([[1, 2, 3], [4, 5, 6]])C = A + Bprint(C)
[[ 2 4 6]
[ 8 10 12]]
Matrix-Scalar Multiplication
A matrix can be multiplied by a scalar represented asC = A . b where b is a scalar. Note: use '*' in Numpy for matrix multiplication
from numpy import arrayA =array([[1, 2, 3], [4, 5, 6]])b =2C = A * bprint(C)
[[ 2 4 6]
[ 8 10 12]]
Matrix-Vector Multiplication
A matrix can be multiplied by a vector represented as C = A . v where v is a vector given it follows the rule of matrix multiplication.
Rule of matrix multiplication
For example, matrix A has the dimensions m rows and n columns and matrix B has the dimensions n and k. The n columns in A and n rows b are equal. The result is a new matrix with m rows and k columns.
Two matrices with the same dimension can be simply multiplied element-wise. Also known as Hadamard Product, it is represented with a circle asC = A o B
Note: Implemented using star operator as in Matrix-Scalar Multiplication
from numpy import arrayA =array([[1, 2, 3], [4, 5, 6]])B =array([[2, 2, 2], [.5, .5, .5]])C = A * Bprint(C)
[[2. 4. 6. ]
[2. 2.5 3. ]]
Matrix-Matrix Multiplication (Dot Product)
Matrix-Matrix, also called the matrix dot product is a complicated multiplication which must follow the rule of matrix multiplication represented asC = A * B.
This is made clear with the following image:
A: 4 x 2; B: 2 x 3; C = A * B => 4 x 3
For calculating:
C12(marked with red arrow) = a11*b12 + a12*b22
C33(marked with blue arrow) = a31*b13 + a32*b23