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Concept
Identity matrix
Summary
In linear algebra, the identity matrix of size n is the n\times n square matrix with ones on the main diagonal and zeros elsewhere. It has unique properties, for example when the identity matrix represents a geometric transformation, the object remains unchanged by the transformation. In other contexts, it is analogous to multiplying by the number 1.
Terminology and notation
The identity matrix is often denoted by I_n, or simply by I if the size is immaterial or can be trivially determined by the context.
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}.
The term unit matrix has a
Official source
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