Editing Identity matrix (section)

==Terminology and notation==
The identity matrix is often denoted by <math>I_n</math>, or simply by <math>I</math> if the size is immaterial or can be trivially determined by the context.<ref>{{Cite web|title=Identity matrix: intro to identity matrices (article)| url=https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:matrices/x9e81a4f98389efdf:properties-of-matrix-multiplication/a/intro-to-identity-matrices | access-date=2020-08-14| website=Khan Academy| language=en}}</ref> 

<math display="block">
I_1 = \begin{bmatrix} 1 \end{bmatrix}
,\ 
I_2 = \begin{bmatrix}
1 & 0 \\
0 & 1 \end{bmatrix}
,\ 
I_3 = \begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1 \end{bmatrix}
,\ \dots ,\ 
I_n = \begin{bmatrix}
1 & 0 & 0 & \cdots & 0 \\
0 & 1 & 0 & \cdots & 0 \\
0 & 0 & 1 & \cdots & 0 \\
\vdots & \vdots & \vdots & \ddots & \vdots \\
0 & 0 & 0 & \cdots & 1 \end{bmatrix}.
</math>

The term '''unit matrix''' has also been widely used,<ref name=pipes>{{cite book |title=Matrix Methods for Engineering |series=Prentice-Hall International Series in Applied Mathematics |first=Louis Albert |last=Pipes |publisher=Prentice-Hall |year=1963 |page=91 |url=https://books.google.com/books?id=rJNRAAAAMAAJ&pg=PA91 }}</ref><ref>[[Roger Godement]], ''Algebra'', 1968.</ref><ref>[[ISO 80000-2]]:2009.</ref><ref>[[Ken Stroud]], ''Engineering Mathematics'', 2013.</ref> but the term ''identity matrix'' is now standard.<ref>[[ISO 80000-2]]:2019.</ref>  The term ''unit matrix'' is ambiguous, because it is also used for a [[matrix of ones]] and for any [[unit (ring theory)|unit]] of the [[matrix ring|ring of all <math>n\times n</math> matrices]].<ref>{{Cite web| last=Weisstein|first=Eric W.| title=Unit Matrix|url=https://mathworld.wolfram.com/UnitMatrix.html|access-date=2021-05-05| website=mathworld.wolfram.com| language=en}}</ref>

In some fields, such as [[group theory]] or [[quantum mechanics]], the identity matrix is sometimes denoted by a boldface one, <math>\mathbf{1}</math>, or called "id" (short for identity). Less frequently, some mathematics books use <math>U</math> or <math>E</math> to represent the identity matrix, standing for "unit matrix"<ref name=pipes /> and the German word {{lang|de|Einheitsmatrix}} respectively.<ref name=":0">{{Cite web| last=Weisstein|first=Eric W.|title=Identity Matrix | url=https://mathworld.wolfram.com/IdentityMatrix.html|access-date=2020-08-14 | website=mathworld.wolfram.com | language=en}}</ref>

In terms of a notation that is sometimes used to concisely describe [[diagonal matrix|diagonal matrices]], the identity matrix can be written as
<math display=block> I_n = \operatorname{diag}(1, 1, \dots, 1).</math>
The identity matrix can also be written using the [[Kronecker delta]] notation:<ref name=":0" />
<math display=block>(I_n)_{ij} = \delta_{ij}.</math>