8.6 Identity Matrix

Types: N/A
Examples: N/A
Constructions: N/A
Generalizations: 8.5 Diagonal Matrix

Properties: N/A
Sufficiencies: N/A
Questions: N/A

Identity Matrix

Let $I_{n} \in R^{n \times n}$ be a square, 8.5 Diagonal Matrix whose diagonal entries are equal to 1 (nondiagonal entries are zero).

I_{n} = [\begin{matrix} 1 & 0 & \dots & 0 \\ 0 & 1 & ⋱ & ⋮ \\ ⋮ & ⋱ & ⋱ & 0 \\ 0 & \dots & 0 & 1 \end{matrix}]

In this case, we define the identity matrix using the individual coefficients as follows

I_{n} (i, k) = {\begin{cases} 1 & if i = k, \\ 0 & if i \neq k . \end{cases}

Remark. The identity matrix is to matrix arithmetic as the identity property is to ordinary arithmetic ( $n \times 1 = n$ )
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