query: Given P idempotent, show that I−P is idempotent.
positive_passages.docid: 147611
positive_passages.text: Given $P$ idempotent, show that $I-P$ is idempotent.
negative_passages.docid: 17031
negative_passages.text: Idempotent linear operators are projections
negative_passages.docid: 62755
negative_passages.text: The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
negative_passages.docid: 42528
negative_passages.text: Prove that every idempotent element is not nilpotent element.
negative_passages.docid: 151985
negative_passages.text: If $p$ is a prime and $x,y \in \mathbb{Z}$, then $(x+y)^p \equiv x^p+y^p \pmod{p}$
negative_passages.docid: 29251
negative_passages.text: Show that the square of any prime number is the Factof of some integer
negative_passages.docid: 60674
negative_passages.text: Finitely generated idempotent ideals are principal: proof without using Nakayama's lemma
negative_passages.docid: 129163
negative_passages.text: Showing that every positive integer can be represented in this form
negative_passages.docid: 154076
negative_passages.text: How to show this property of $\mathbb{RP}^{n}$.
negative_passages.docid: 7034
negative_passages.text: Prove that $A+I$ is invertible if $A$ is nilpotent
negative_passages.docid: 57543
negative_passages.text: Show that a matrix is nilpotent.
negative_passages.docid: 145879
negative_passages.text: $R$ is PID, so $R/I$ is PID, and application on $\mathbb{Z}$ and $\mathbb{N}$
negative_passages.docid: 4912
negative_passages.text: Show that an infinite set $C$ is equipotent to its cartesian product $C\times C$
negative_passages.docid: 124424
negative_passages.text: How to show that there is a deduction of $\varphi\leftrightarrow\psi$
negative_passages.docid: 7802
negative_passages.text: Showing $\prod\limits_{i<j} \frac{x_i-x_j}{i-j}$ is an integer
negative_passages.docid: 27086
negative_passages.text: proof for $\langle q| p \rangle = e^{ipq}$
negative_passages.docid: 158426
negative_passages.text: Proving lemma about centrality of idempotent elements in a Ring with no nilpotent elements.