R Academy · Lesson

Matrix Arithmetic and Operations

Perform element-wise and matrix multiplication, addition, and subtraction.

Element-wise vs Matrix Operations

R distinguishes between element-wise operations (using +, -, *, /) and true matrix operations (using %*%). Understanding this difference is critical for correct linear algebra.

A <- matrix(c(1,2,3,4), nrow = 2)
B <- matrix(c(5,6,7,8), nrow = 2)
cat('A:
'); print(A)
cat('B:
'); print(B)

# Element-wise multiply
cat('A * B (element-wise):
'); print(A * B)
# Matrix multiply
cat('A %*% B (matrix mult):
'); print(A %*% B)

Element-wise Addition and Subtraction

+ and - between two matrices of the same dimensions add or subtract corresponding elements. These are purely element-wise operations.

# Monthly revenue vs target (in thousands)
revenue <- matrix(c(120,135,110,98, 145,160,132,115),
                  nrow = 2, byrow = TRUE)
target  <- matrix(c(130,130,130,130, 150,150,150,150),
                  nrow = 2, byrow = TRUE)

deviation <- revenue - target
cat('Revenue vs Target deviation:
')
print(deviation)
cat('Above target?:
')
print(revenue >= target)

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