On Oct 12, 2011, at 12:04 AM, Rolf Turner wrote:
> On 12/10/11 08:31, Timothy Bates wrote:
>> To do matrix multiplication: m x n, the Rows and columns of m must be equal
>> to the columns and rows of n, respectively.
> No. The number of columns of m must equal the number of rows of n,
> that's all. The number of *rows* of m and the number of *columns* of n
> can be anything you like.
>
Yes, I don't know how I wrote that.. conflating criteria for conformability
with the shape of the output,,,
The easiest way to remember this is to visualize the dimensions of the two
matrices side by side:
R1 C1 %*% R2 C2
The adjacent numbers must match (C1 & R2)
The resultant matrix will have dimensions of the outside numbers (R1 C2).
i.e.,
A = matrix(1:4,nrow=1); B = matrix(1:4,ncol=1); A; B; A %*% B; B %*% A
A
[,1] [,2] [,3] [,4]
[1,] 1 2 3 4
B
[,1]
[1,] 1
[2,] 2
[3,] 3
[4,] 4
A %*% B
[,1]
[1,] 30
B %*% A
[,1] [,2] [,3] [,4]
[1,] 1 2 3 4
[2,] 2 4 6 8
[3,] 3 6 9 12
[4,] 4 8 12 16
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