# Transpose a Matrix in Clojure

Imagine rows of letters, numbers, and Greek letters:

```plaintext
[[:a :b]
 [:1 :2]
 [:alpha :beta]]
```

Now, you want to transpose them. You started with a vector of vectors. Clojure's [`map`](https://clojuredocs.org/clojure.core/map) function is pretty amazing::

> *   (map f)
>     
> *   (map f coll)
>     
> *   (map f c1 c2)
>     
> *   (map f c1 c2 c3)
>     
> *   (map f c1 c2 c3 & colls)
>     
> 
> Returns a lazy sequence consisting of the result of applying f to the set of first items of each coll, followed by applying f to the set of second items in each coll, until any one of the colls is exhausted. Any remaining items in other colls are ignored. Function f should accept number-of-colls arguments. Returns a transducer when no collection is provided.

Normally, I think of this arity of `map`: `(map f coll)`. In your case, you have three collections, so you'll make use of `(map f c1 c2 c3)`. You want to stick with vectors, so you'll use `mapv`, which has the same semantics.

If you ignore the outer vector, you can use `mapv` with `vector`:

```clojure
(mapv vector [:a :b] [:1 :2] [:alpha :beta])
;;=> [[:a :1 :alpha]
;;    [:b :2 :beta]]
```

You don’t have to omit the outer vector thanks to the magic of [`apply`](https://clojuredocs.org/clojure.core/apply), which allows you to pass a collection of arguments to a function that wants individual arguments:

```clojure
(apply mapv vector [[:a :b] [:1 :2] [:alpha :beta]])
;;=> [[:a :1 :alpha]
;;    [:b :2 :beta]]
```

This is amazing.