Matrix multiplication in q lang

Following my previous post, I’ve started reading the book “Q for Mortals”. It’s a fascinating book and I highly recommend it to anyone who is interested in learning this language properly. After getting through chapter 1 and realizing how well q-lang handles lists and vectors (considering it’s a vector-language), I started thinking what I need to do to write the matrix multiplication operator in q-lang. But I don’t want to just write it. I mean writing it in a for loop is easy and all, but I want to write it as compact as I can. I tried my best to condense the entire code into a one-liner, but failed. It turned into 2 lines . Anyways, here it goes.

Consider the $m \times n$ matrix \(A\) and the \(n \times p\) matrix \(B\). Let’s create some simple examples for \(A\) and \(B\).

a:(1 2 3; 2 3 4)
b:(3 5; 4 6; 5 7)

Here a is \(2 \times 3\) while b is \(3 \times 2\). Let’s see what happens if I multiply one row of a by b

a[0]*b
// shows:
// 3  5 
// 8  12
// 15 21

which is multiplying the first row of a by each column in b. Now if we sum this, we get

sum a[0]:b
// shows:
// 26 38

which is the first row of the result of the matrix multiplication \(A \times B\). See where this is going? Now we just need to repeat this for each row in a. We can use “each-left” to achieve this, but we need to define this row-times-matrix operation first.

row_mult:{[row;matrix] sum row*matrix}

Now we can use each-left as

a row_mult\: b
// shows:
// 26 38
// 38 56

which is the full result of the matrix multiplication. Yay!