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Identity matrix

Overview#

Identity matrix (or sometimes ambiguously called a unit matrix), of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere and is often denoted by In, or simply by I.

Identity matrix/identity-matrix.png

The Identity matrix itself is invertible, being its own inverse

The Identity matrix of a given size is the only idempotent matrix of that size having full rank. That is, Identity matrix is the only matrix such that:

  • when multiplied by itself the result is itself
  • all of its rows, and all of its columns, are linearly independent.

The principal square root of an Identity matrix is itself, and this is its only positive definite square root. Every Identity matrix with at least two rows and columns has an infinitude of symmetric square roots.

More Information#

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