query: what does mean that $A^TPA+P=I$?
positive_passages.docid: 156438
positive_passages.text: Find a matrix equation equivalent to $A^TPA+P=I$
negative_passages.docid: 38636
negative_passages.text: A basic question about exponentiation: when is $a^{xy}=(a^x)^y$?
negative_passages.docid: 88687
negative_passages.text: Proof of the inequality $||a+b|^p - |a|^p| \leq \epsilon |a|^p + C_{\epsilon} |b|^p$
negative_passages.docid: 155828
negative_passages.text: How do I show that $A$ and $A^T$ are similar, given that the minimal polynomial of $A$ splits over $\mathbb{F}$?
negative_passages.docid: 127205
negative_passages.text: Explain proof of irreducibility of $x^{p-1} + 2x^{p-2}+ \dots +(p-1)x + p$
negative_passages.docid: 36567
negative_passages.text: $A^{T}A$ positive definite then A is invertible?
negative_passages.docid: 104258
negative_passages.text: Proof Verification: $\dim\mathrm{Im} T+\dim\ker T=\dim V$
negative_passages.docid: 118417
negative_passages.text: Is $AA^T$ positive semidefinite?
negative_passages.docid: 13833
negative_passages.text: What is the coefficient of the term $a^i b^j c^k$ in the expansion of $(a+b+c)^n$?
negative_passages.docid: 102234
negative_passages.text: Show $a^p \equiv a \mod 2p$
negative_passages.docid: 64453
negative_passages.text: Prove if $(a,p)=1$, then $\{a,2a,3a,...,pa\}$ is a complete residue system modulo $p$.
negative_passages.docid: 55377
negative_passages.text: Non-zero eigenvalues of $AA^T$ and $A^TA$
negative_passages.docid: 149022
negative_passages.text: In Markov inequality proof, why is $\int_a^\infty xp(x) \, dx \ge \int_a^\infty ap(x) \, dx$
negative_passages.docid: 41300
negative_passages.text: Show $(x+y)^a > x^a + y^a$ for $x,y>0$ and $a>1$
negative_passages.docid: 112707
negative_passages.text: Must $Q^\mathsf{T}Q = I$ if $(Qx)^\mathsf{T}(Qx) = x^\mathsf{T}x$
negative_passages.docid: 55018
negative_passages.text: Prove that $A^*A + I$ is invertible
negative_passages.docid: 150320
negative_passages.text: Why does $a^{b}·a^{c}=a^{b+c}$?