Let u be a unit vector, and P = Identity vector − u⊗u. Compute P^2 and...

Let u be a unit vector, and P = Identity vector − u⊗u. Compute P^2 and P^(−1).

Hint: Rank one Matrix.

Solutions

Expert Solution

The outer product is equivalent to the matrix multiplication that is

where is the transpose of . Since is a unit vector,

Now,

is idempotent and which means is non-identity idempotent matrix.

Now we know that only non-singular idempotent matrix is the identity matrix. All the non-identity idempotent matrix are singular and hence does not invertible. So, does not exist in the present case.

Colby Messinger answered 1 month ago

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