- #31
- 15,524
- 769
Of course.
In order for the square of a matrix to be equal to the matrix
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For a matrix A to satisfy the condition A² = A, it must be idempotent, meaning it retains its form when squared. The discussion highlights that A can either be the identity matrix or a singular matrix, with the identity matrix being the only non-singular idempotent matrix. It is established that diagonal idempotent matrices have entries of either 0 or 1, and any singular idempotent matrix must have at least one zero eigenvalue. The conclusion drawn is that if A is idempotent and not the identity matrix, it must be singular. The participants emphasize the importance of understanding the properties of singular and non-singular matrices in this context.