# What is the motivation behind naming identity matrix as "eye"?

Matlab, as well as some other PLs (e.g. Python's numpy package) use "eye" as a function name for creation of the identity matrix. Why is that so?

• isn't it just to avoid a single letter like "I" for a built-in? Dec 6, 2018 at 11:50
• @postmortes, maybe. But I'm personally seeing this "eye" as a biological organ. Perhaps that is because I'm not a native English speaker. I just wonder Dec 6, 2018 at 11:52
• ah, "eye" is sometimes used to 'spell' I in English; Similarly h is 'spelled' aitch, and f is spelled eff. Probably not something you'd know if you weren't a native speaker though Dec 6, 2018 at 11:55
• @postmortes, don't you want to post that as an answer please? Dec 6, 2018 at 11:58
• John Lawler, a fairly respectable linguist, gives the list here ( groups.google.com/forum/#!topic/alt.usage.english/LZRjRbMHPe8 ) in a 1996 usenet post. @JDoe if I get any time at all this afternoon I'll pull this all together into an answer, but I expect someone will beat me to it Dec 6, 2018 at 14:40

In Matlab, i is treated as a function (see https://www.mathworks.com/help/matlab/ref/i.html ) returning the imaginary unit $$\sqrt{-1}$$. To avoid confusion with that, eye is used to represent the unit matrix. I couldn't find any documentation on the mathworks site explaining the choice, but the likely answer is that it's because eye is used in English as a way to spell the name of the letter 'I'.

The 'spelling-names' for English letters are given by John Lawler in this post (https://groups.google.com/forum/#!topic/alt.usage.english/LZRjRbMHPe8 ), and listed below for convenient reference.

 a  /e/       A [cap preferred]
b  /bi/      B [ditto; 'bee' more common than 'be']
c  /si/      C [  ", 'see'; but 'C-note' and 'cee-note' both occur]
d  /di/      dee
e  /i/       ee or E
f  /ef/      ef, or eff ['you effing idiot!']
g  /ji/      gee ['jee' is possible but not recommended]
h  /ec^/     aitch [the 't' seems to be required]
i  /ay/      I or aye, occasionally 'eye'; cf 'eye-dialect'
j  /je/      jay
k  /ke/      kay
l  /El/      el, or ell
m  /Em/      em [cf em-dash]
n  /En/      en [cf en-dash]
o  /o/       oh or owe ['ow' makes more sense but is already /aw/]
p  /pi/      P ['pee' is less common, because of its vulgar homophone]
q  /kyu/     queue, or cue [not recommended]
r  /ar/      are? ar? ahr? arr?  nothing looks good; use R
s  /es/      es or ess
t  /ti/      tee
u  /yu/      you, or yoo
v  /vi/      vee [delta-vee, or dee-vee]
w  /d@b@lyu/ double-u or doubleyou
x  /Eks/     ex  [shorter to spell than to pronounce!]
y  /way/     why, or wye
z  /zi/      zee [US usage; elsewhere zed]
Spelling the letter names is not frequent enough in written English to be standard.  There's
lots of variation.
`

As noted in both John Lawler's list and timtfj's comment, some of the letter names have taken on lives of their own, with em- and en-dash occuring in printing and denoting the width of a capital M or capital N in the chosen font.