Addition of matrices

Definition

For general matrices A and B

the addition operator is defined if and only if they have the same order; m₁ = m₂ = m and n₁ = n₂ = n.

Matrix addition is an example of binary operation on the set of matrices of the same order.

plus operator

Import the plus operator in the namespace by doing

=> (require '[kigubkur.op [plus :refer [plus]]])

Examples using plus

Example 1

=> (def A [[2 4]
           [3 2]])
=> (def B [[1 3]
           [-2 5]])
=> (plus A B)
[[3 7]
 [1 7]]

Example 2

=> (def A [[3 1 -1]
           [2 3 0]])
=> (def B [[2 5 1]
           [-2 3 (/ 1 2)]])
=> (plus A B)
[[5 6 0]
 [0 6 1/2]]

Example 3

=> (def A [[-1 4 -6]
           [8 5 16]
           [2 8 5]])
=> (def B [[12 7 6]
           [8 0 5]
           [3 2 4]])
=> (plus A B)
[[11 11 0]
 [16 5 21]
 [5 10 9]]

Example 4

=> (def A [[1 2 -3]
           [5 0 2]
           [1 -1 1]])
=> (def B [[3 -1 2]
           [4 2 5]
           [2 0 3]])
=> (plus A B)
[[4 1 -1]
 [9 2 7]
 [3 -1 4]]

Basic properties of matrix addition

Given,

General form	Example

1. Commutative Law

=> (def A [[80 60]
           [75 65]
           [90 85]])
=> (def B [[90 50]
           [70 55]
           [75 75]])
=> (= (plus A B) (plus B A))
true

2. Associative Law

=> (def C [[95 70]
           [70 60]
           [80 70]])
=> (= (plus (plus A B) C) (plus A (plus B C)))
true

3. Existence of additive identity

=> (def O [[0 0]
           [0 0]
           [0 0]])
=> (= (plus A O) (plus O A) A)
true

4. The existence of additive inverse

=> (def minusA [[-80 -60]
           [-75 -65]
           [-90 -85]])
=> (= (plus A minusA) (plus minusA A) O)
true