# Construct the Identity Matrix

The challenge is very simple. Given an integer input n, output the n x n identity matrix. The identity matrix is one that has 1s spanning from the top left down to the bottom right. You will write a program or a function that will return or output the identity matrix you constructed. Your output may be a 2D array, or numbers separated by spaces/tabs and newlines.

Example input and output

1: [[1]]
2: [[1, 0], [0, 1]]
3: [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
4: [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]
5: [[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]]

1
===
1

2
===
1 0
0 1

3
===
1 0 0
0 1 0
0 0 1

etc.


This is , so the shortest code in bytes wins.

• Given an integer input n ... -- I assume you mean a natural number? – Jonathan Frech Aug 28 '18 at 17:00

# MATL, 2 bytes

Xy


A translation of my Octave answer.

Try it online.

A 4 byte version with no built-ins (thanks to Luis Mendo):

:t!=
:     take input n and a generate row array [1,2,...n]
t    duplicate
!   zip
=  thread compare over the result

• It must have been difficult, to translate this very sophisticated code :D – flawr Jan 28 '16 at 18:40
• @flawr You have no idea. This is truly my masterpiece. – a spaghetto Jan 28 '16 at 18:40
• – Conor O'Brien Jan 28 '16 at 18:42
• Now I see why you were asking! :-D – Luis Mendo Jan 28 '16 at 18:54
• Without builtins: :t!= – Luis Mendo Jan 28 '16 at 18:56

## TI-BASIC, 2 bytes

identity(Ans


Fun fact: The shortest way to get a list {N,N} is dim(identity(N.

Here's the shortest way without the builtin, in 8 bytes:

randM(Ans,Ans)^0


randM( creates a random matrix with entries all integers between -9 and 9 inclusive (that sounds oddly specific because it is). We then take this matrix to the 0th power.

• "that sounds oddly specific because it is" TI-BASIC is weird. O_o – Doorknob Jan 29 '16 at 13:48
• Hell yes. TI-BASIC. +1 – bearacuda13 Jun 30 '17 at 19:40
• isn't the shortest way to get a list {N,N}, umm, {N,N}? – Cyoce Jul 2 '17 at 23:05
• @Cyoce No; dim( and identity( are each one byte because TI-BASIC is tokenized. – lirtosiast Jul 3 '17 at 21:45

# Julia, 9 3 bytes

eye


This is just a built-in function that accepts an integer n and returns an nxn Array{Float64,2} (i.e. a 2D array). Call it like eye(n).

Note that submissions of this form are acceptable per this policy.

• I see what you did there! Nice one! – Ismael Miguel Jan 29 '16 at 21:41
• This also works in Math.JS – ATaco Jun 29 '17 at 6:53

# APL, 5 bytes

∘.=⍨⍳


This is a monadic function train that accepts an integer on the right and returns the identity matrix.

Try it here

# Octave, 10 4 bytes

@eye


Returns an anonymous function that takes a number n and returns the identity matrix.

• @eye is sufficient. – flawr Jan 28 '16 at 18:37
• @flawr Thanks, I knew there was a way to do it like that but I always forget :P – a spaghetto Jan 28 '16 at 18:39
• eye produces the identity matrix in a lot/some numerically oriented languages. – flawr Jan 28 '16 at 18:50
• What does the @ do? – Cyoce Jul 2 '17 at 23:06
• @Cyoce @ is the "function handle operator", it works like a lambda and also as a reference to a particular function, so for instance, @(x)x.^2 is the squaring function and @sqrt is a reference to the square root function. You can read more about that here – Giuseppe Jan 3 '18 at 18:29

# R, 4 bytes

diag


When given a matrix, diag returns the diagonal of the matrix. However, when given an integer n, diag(n) returns the identity matrix.

Try it online

## Python 2, 42 bytes

lambda n:zip(*[iter(([1]+[0]*n)*n)]*n)[:n]


An anonymous function, produces output like [(1, 0, 0), (0, 1, 0), (0, 0, 1)],

First, creates the list ([1]+[0]*n)*n, which for n=3 looks like

[1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]


Using the zip/iter trick zip(*[iter(_)]*n to make groups of n gives

[(1, 0, 0), (0, 1, 0), (0, 0, 1), (0, 0, 0)]


Note that the 1 comes one index later each time, giving the identity matrix. But, there's an extra all-zero row, which is removed with [:n].

• Damn that zip/iter trick is ingenious – seequ Feb 9 '16 at 20:58

# Jelly, 4 bytes

R=€R


Doesn't use a built-in. Try it online!

### How it works

R=€R    Main link. Input: n

R       Range; yield [1, ..., n].
R    Range; yield [1, ..., n].
=€     Compare each.
This compares each element of the left list with the right list, so it
yields [1 = [1, ..., n], ..., n = [1, ..., n]], where comparison is
performed on the integers.

• This code is unacceptably long. – flawr Jan 28 '16 at 18:53
• @flawr Twice the length of the shortest one. That's indeed an unusual encounter. – Rainer P. Jan 28 '16 at 18:55
• @flawr Yes, and no shorter than J. FAIL! – Adám Feb 10 '16 at 15:27
• In modern versions of Jelly, =þ is two bytes, and makes fun of the longer answers. – Lynn Aug 19 '16 at 9:57
• @Lynn That's still twice as long as the shortest oneS. – Adám Aug 21 '16 at 18:29

# J, 4 bytes

=@i.


This is a function that takes an integer and returns the matrix.

• I think you can do it in 3: =i. – Sam Elliott Sep 21 '16 at 18:39
• @SamElliott that doesn't work. For example, (=i.) 10 => 0 0 0 0 0 0 0 0 0 0 – Cyoce Jul 3 '17 at 0:03

f n=[[0^abs(x-y)|y<-[1..n]]|x<-[1..n]]


Pretty straightforward, though I think one can do better (without a language that already has this function built in, as many have done).

Edit: dropped some bytes thanks to Ørjan Johansen

• You can cheat the fromEnum as sum[1|x==y]. – xnor Jan 29 '16 at 0:31
• pretty sure you can remove the space in fromEnum (y==x) – Cyoce Jul 2 '17 at 23:07
• @xnor One byte shorter than that: 0^abs(x-y). – Ørjan Johansen Jan 3 '18 at 16:56
• @xnor Oh, you just used 0^(x-y)^2 yourself in another answer, even shorter. – Ørjan Johansen Jan 3 '18 at 18:12
• @ØrjanJohansen Yes, seeing your comment was nice timing :) – xnor Jan 3 '18 at 18:16

# Pyth, 7 bytes

XRm0Q1Q


Try it online: Demonstration

Creating a matrix of zeros and replacing the diagonal elements with ones.

• You can save one byte by removing the final Q – Jim Jun 22 '17 at 18:43
• @jim Thanks, but that would actually be not allowed. The feature (implicit Q at the end) was implemented after the challenge was posted. – Jakube Jun 22 '17 at 22:40

# JavaScript ES6, 6862 52 bytes

Saved 10 bytes thanks to a neat trick from @Neil

x=>[...Array(x)].map((_,y,x)=>x.map((_,z)=>+(y==z)))


Trying a different approach than @Cᴏɴᴏʀ O'Bʀɪᴇɴ's. Could possibly be improved.

• This was exactly what I wrote before I scrolled down to find out that you'd beaten me to it. – Neil Jan 28 '16 at 19:57
• So, in response to your challenge, I give you the (in hindsight) obvious x=>[...Array(x)].map((_,y,x)=>x.map((_,z)=>+(y==z))) for a saving of 10 bytes. – Neil Jan 28 '16 at 19:59
• @Neil Thanks a lot! I'll mention that it's your trick in the answer. – ETHproductions Jan 28 '16 at 20:12
• x=>[...Array(x)].map((_,y,x)=>x.map(_=>+!y--)) – l4m2 Apr 25 '18 at 17:47

# Retina, 25

Credit to @randomra and @Martin for extra golfing.

\B.
0
+(.*) 00¶0 $1  Try it online. Note this takes input as a unary. If this is not acceptable, then decimal input may be given as follows: # Retina, 34 .+$0$*1 \B. 0 +(.*) 0$
$0¶0$1


Try it online.

• ...whoa. Retina is becoming powerful as a language for more than regex. – ETHproductions Jan 28 '16 at 21:02
• @ETHproductions yes, though this is answer pretty much all regex substitution. The only special thing is the use of $*0 to replace a number n with n 0s. – Digital Trauma Jan 28 '16 at 21:06 # Haskell, 54 bytes (#)=replicate f n=map(\x->x#0++[1]++(n-x-1)#0)[0..n-1]  f returns the identity matrix for input n. Far from optimal. • You can save a handful of bytes using a list comprehension instead of a map call. – MathematicalOrchid Jan 29 '16 at 9:23 # Lua, 77 75 65 bytes x,v=z.rep,io.read()for a=1,v do print(x(0,a-1)..'1'..x(0,v-a))end  Well, I'm not sure if lua is the best language for this with the two period concatenation... But hey, there's a shot at it. I'll see if there's any improvements to be made. EDIT: I figured something out on accident which I find rather odd, but, it works. In Lua, everyone knows you have the ability to assign functions to variables. This is one of the more useful CodeGolf features. This means instead of: string.sub("50", 1, 1) -- = 5 string.sub("50", 2, 2) -- = 0 string.sub("40", 1, 1) -- = 4 string.sub("40", 2, 2) -- = 0  You can do this: s = string.sub s("50", 1, 1) -- = 5 s("50", 2, 2) -- = 0 s("40", 1, 1) -- = 4 s("40", 2, 2) -- = 0  But wait, Lua allows some amount of OOP. So you could potentially even do: z="" s = z.sub s("50", 1, 1) -- = 5 s("50", 2, 2) -- = 0 s("40", 1, 1) -- = 4 s("40", 2, 2) -- = 0  That will work as well and cuts characters. Now here comes the weird part. You don't even need to assign a string at any point. Simply doing: s = z.sub s("50", 1, 1) -- = 5 s("50", 2, 2) -- = 0 s("40", 1, 1) -- = 4 s("40", 2, 2) -- = 0  Will work. So you can visually see the difference, take a look at the golfed results of this: Using string.sub (88 characters) string.sub("50", 1, 1)string.sub("50", 2, 2)string.sub("40", 1, 1)string.sub("40", 2, 2)  Assigning string.sub to a variable (65 characters) s=string.sub s("50", 1, 1)s("50", 2, 2)s("40", 1, 1)s("40", 2, 2)  Assigning string.sub using an OOP approach (64 characters) z=""s=z.sub s("50", 1, 1)s("50", 2, 2)s("40", 1, 1)s("40", 2, 2)  Assigning string.sub using a.. nil approach? (60 characters) s=z.sub s("50", 1, 1)s("50", 2, 2)s("40", 1, 1)s("40", 2, 2)  If someone knows why this works, I'd be interested. • The "z.rep" line is breaking on mine. I'm betting there should be a z='' somewhere? A shorter variant of z=''z.rep would just be ('').rep . You can also use the cmdline ... for reading input, and widdle the bytecount down to 57 as follows: z='0'for i=1,...do print(z:rep(i-1)..1 ..z:rep(...-i))end – thenumbernine Mar 22 '16 at 11:39 • I found someone suggesting ("").rep before, but I was unable to get it to work. It'd always error out. Maybe my interpreter is the problem here. I'm struggling to find any documentation on this command line input, do you know where it can be found? – Skyl3r Mar 23 '16 at 12:51 # Python 3, 48 Saved 1 byte thanks to sp3000. I love challenges I can solve in one line. Pretty simple, build a line out of 1 and 0 equal to the length of the int passed in. Outputs as a 2d array. If you wrap the part after the : in '\n'.join(), it'll pretty print it. lambda x:[[0]*i+[1]+[0]*(x+~i)for i in range(x)]  • x-i-1 -> x+~i – Sp3000 Jan 28 '16 at 21:58 # C, 59 or 59 56 or 56 Two versions of identical length. 3 bytes saved due to suggestion from anatolyg: (n+1) --> ~n Iterates i from n*n-1 to zero. Prints a 1 if i%(n+1) is zero, otherwise 0. Then prints a newline if i%n=0 otherwise a space. i;f(n){for(i=n*n;i--;)printf(i%n?"%d ":"%d\n",!(i%~n));} i;f(n){for(i=n*n;i--;)printf("%d%c",!(i%~n),i%n?32:10);}  • n+1 is too dull. Use ~n instead! – anatolyg Jan 29 '16 at 0:23 • Thanks! I should have spotted that, because it occured to me when I looked at NBZ's challenge today. – Level River St Jan 29 '16 at 0:31 • I'm not too familiar with C. What does i; do? – Cyoce Aug 20 '16 at 22:56 • @Cyoce i; just declares the variable i. In C you always have to declare a variable before using it, indicating the type so the compiler knows how much memory to allocate. With the GCC compiler, if you don't specify a type it is assumed to be int. – Level River St Aug 21 '16 at 0:55 • You can take 1 more byte off of the second one, since tabs are allowed, you can replace 32, with 9. – Bijan Mar 29 '17 at 22:40 # Mata, 4 bytes I(3)  Output [symmetric] 1 2 3 +-------------+ 1 | 1 | 2 | 0 1 | 3 | 0 0 1 | +-------------+  Mata is the matrix programming language available within the Stata statistical package. I(n) creates an identity matrix of size n*n • Welcome to Programming Puzzles and Code Golf Stack Exchange. This is a good answer; (ab)use of built-ins is great for golfing. I noticed that your answer is actually 1 byte: I, and the other 3 bytes are just calling the function. That would make your answer one of the lowest on this challenge! :-) – wizzwizz4 Aug 19 '16 at 10:43 # K6, 1 byte =  = is exactly this Try it online! ## Pyth, 8 bytes mmsqdkQQ  Try it here. • I must say, it's highly unusual that the Pyth answer is four times longer than the shortest answer... – ETHproductions Jan 28 '16 at 21:01 • Hrm, this was the best I was able to get that looks 100% valid, but I did find qRRQQ which seems to work except you get True and False instead of 1 and 0, however fixing this afaik requires using three bytes for sMM which doesn't help... – FryAmTheEggman Jan 28 '16 at 21:11 • @FryAmTheEggman I also found qRRQQ. I've tried a number of other programs, and none of them were shorter. – lirtosiast Jan 28 '16 at 21:12 # Python 3.5 with NumPy - 5749 30 bytes import numpy numpy.identity  NumPy.identity takes in an integer, n, and returns a n by n identity matrix. This answer is allowable via this policy. • Actually I believeimport numpy\nnumpy.identityis a legitimate answer. – FryAmTheEggman Jan 28 '16 at 21:49 • Thanks for the tip @MorganThrapp! And @FryAmTheEggman, you mean that my answer could just be import numpy\nnumpy.identity() which is 30 bytes? – linkian209 Jan 29 '16 at 20:09 • I got so confused by \nnumpy lol... This would also be valid, @FryAmTheEggman, no? from numpy import identity. 26 bytes. – Ogaday Feb 3 '16 at 16:53 • Also, see my answer something similar – Ogaday Feb 3 '16 at 17:00 • @Ogaday I don't think that is correct, the line you've given does not evaluate to a function. You would need to do from numpy import identidy\nidentity (in which case it would be shorter to use * instead of the specific builtin) – FryAmTheEggman Feb 3 '16 at 17:53 # Mathematica, 35 Bytes without using IdentityMatrix Table[Boole[i==j],{i,1,#},{j,1,#}]&  ## Javascript, 40 f= n=>'0'.repeat(n).replace(/./g,"$1$'\n") I.oninput=_=>O.innerHTML=f(+I.value) I.oninput() <input id=I value=5> <pre id=O> # Japt, 1412 10 bytes Uo £Z®¥X|0  Test it online! Note: this version has a few extra bytes to pretty-print the output. Uo £Z®¥X|0 // Implicit: U = input integer Uo £ // Create the range [0..U). Map each item X and the full array Z to: Z® // Take the full array Z, and map each item Z to: ¥X|0 // (X == Z) converted to a number. 1 for equal, 0 for non-equal. // Implicit: output result of last expression  # Brain-Flak, 206170 162 bytes (([{}])){({}<>(())<><(({})<{({}()(<>)<>)}{}>)>)}{}(({}<><(())>)){({}()<({[()]<({}()<({}<>((((()()()()){}){}){})((()()()()){}){})<>>)>}{})>)<>((()()()()()){})<>}<>  Try it online! # K, 7 bytes t=\:t:!  Take the equality cross product of two vectors containing [0,n). In action:  t=\:t:!3 (1 0 0 0 1 0 0 0 1) t=\:t:!5 (1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1)  # Java, 60 bytes n->{int[][]i=new int[n][n];for(;n-->0;)i[n][n]=1;return i;};  Creates a 2D array and replaces elements where row and column are equal with 1. • You don't have to add the trailing semicolon to the byte-count for Java lambda answers. – Kevin Cruijssen Jun 29 '17 at 14:20 # CJam, 7 bytes {,_ff=}  This is a code block that pops an integer from the stack and pushes a 2D array in return. Try it online! # Mathematica, 14 bytes IdentityMatrix  Test case IdentityMatrix[4] (* {{1,0,0,0},{0,1,0,0},{0,0,1,0},{0,0,0,1}} *)  ## Perl, 39 33 bytes /$/,say map$==$_|0,@%for@%=1..<>


Thanks to Ton Hospel for saving 6 bytes

Running with the -E perlrun:

$echo 3 | perl -E'@%=1..<>;$a=$_,say map{$a==$_|0}@%for@%' 100 010 001  • Golfing a bit more: /$/,say map$==$_|0,@%for@%=1..<> or even better //,say map$'==$_|0,@%for@%=1..<> but like that you can't put it in single quotes anymore – Ton Hospel Mar 8 '16 at 15:51
• @TonHospel Wow thats cool, thanks. The later would require the use of print instead of say, because -E` is only free on the command line. – andlrc Mar 14 '16 at 22:15