Identity Matrix

Types: Not Applicable
Examples: Not Applicable
Constructions: Not Applicable
Generalizations: Not Applicable

Properties: Not Applicable
Sufficiencies: Not Applicable
Equivalences: Not Applicable
Justifications: Not Applicable

Identity Matrix

The identity matrix is the Matrix with 1’s along the main diagonal (the diagonal from top left to bottom right) and 0’s elsewhere.

Example: and .

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Remark: If is an matrix, then
, or, more precisely, ,
since if one must change the size of the identity matrix to match the size of . When the context is clear, we omit the index.

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Remark: The columns of the identity matrix are the standard basis vectors .