CODEWITHSUNDEEP
rmatrix
James ereknrkj
James ereknrkj

Reputation:

Matrix multiplication - loose definition of non-conformable matrices

Suppose we have the following:

x <- matrix(1:9, nrow=3)
y <- c(1,2,3)
x%*%y
y%*%x

Why are the matrix multiplications not undefined? We know that x is a 3 x 3 matrix and y is a 1 x 3 matrix. So x %*% y should not be defined and y %*% x should be a 1 x 3 matrix.

Upvotes: 5

Views: 3553

Answers (1)

Macro
Macro

Reputation: 1510

Luckily (or unfortunately, depending on the situation) many R operators (in their default state) are overloaded and do all sorts of things 'under the hood' - in this example, the default functionality for %*% in R automatically coerces y to matrix whose dimension will work. When you type 

x %*% y

it makes y a 3 x 1 matrix and when you type 

y %*% x

it makes y a 1 x 3 matrix.

Try comparing those with when you type 

x %*% as.matrix(y)

and 

t(as.matrix(y)) %*% x

respectively

Upvotes: 7

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