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3×3 identity matrix
In linear algebra, the identity matrix of size n is the n × nsquare matrix with ones on the main diagonal and zeros elsewhere. It is denoted by In, or simply by I if the size is immaterial or can be trivially determined by the context.
In some fields, such as group theory or quantum mechanics, the identity matrix is sometimes denoted by a boldface one, 1, or called "id" (short for identity); otherwise it is identical to I. Less frequently, some mathematics books use U or E to represent the identity matrix, meaning "unit matrix" and the German word Einheitsmatrix respectively.
The principal square root of an identity matrix is itself, and this is its only positive-definite square root. However, every identity matrix with at least two rows and columns has an infinitude of symmetric square roots.