idempotent ,

Thus for example only a square matrix can be idempotent.

Managing the data state of idempotent services is the only complexity.

An important class of idempotent functions is given by projections in a vector space.

Here we start with 0 in 32-bit single-precision and repeatedly add 1 until the operation is idempotent.

As an illustration, a proof is given below for the idempotent law for union.

One example of an idempotent element is a projection in linear algebra.

If f is idempotent, then the above definitions can be extended to finite sets.

Both the real and complex functions are idempotent.

An idempotent matrix is always diagonalizable and its eigenvalues are either 0 or 1.

Storing a given set of content is usually idempotent, as the final value stored remains the same after each execution.

In a processor where such instructions are not idempotent, dealing with page faults is much more complex.

There may also exist idempotent elements such as (1 + u)/2.

The system is made eventually consistent by requiring that all write operations are idempotent and commutative.

In a load-store architecture, instructions that might possibly cause a page fault are idempotent.

Unlike the interior operator, ext is not idempotent, but the following holds:

A ring in which all elements are idempotent is called a Boolean ring.

Any algebra whose elements are idempotent is also power-associative.

Canceling an order is idempotent, because the order remains canceled no matter how many requests are made.

Furthermore, disjunction is not idempotent and does not distribute over conjunction.

A band is a semigroup the operation of which is idempotent.

As mentioned above, the identity map and the constant maps are always idempotent maps.

It is an example of a closure operator; all closure operators are idempotent functions.

And deleting something is generally idempotent, as the end result is always the absence of the thing deleted.

In fact, the resulting structure is an idempotent monoid.

This means that the operation of pressing a button to make the elevator change floors is an idempotent operation.