Title: Theory / Lost deck
Tags: récupéré

Name: An expansion of \(\mathcal A\)
Definition: A \(\sigma\cup\tau\)-structure, equal to \(\mathfrak A\) for each element of \(\sigma\)
Page: 68
Chapter: 5
Section: 1
Variables: \(\sigma\) a vocabulary,
\(\mathfrak{A}\) a \(\sigma\)-structure
Context: Model theory

Definition: The \(\cup\sigma_i\)-structure, with universe \(A\), and a symbol \(s_j\in\sigma_i\) interpreted as in \(\mathcal A_i\)
Page: 68
Chapter: 5
Section: 1
Variables: \(\sigma_1,\sigma_2\) a vocabulary,
\(\mathfrak{A}_i\) a \(\sigma_i\)-structure
Notation: \((\mathcal A_1,\mathcal A_2)\)
Assuming: Both structures have the same universe

Name: Orthogonal linear transformations
Definition: \(\sum\left(a_i^{j}\right)^2=1\)
Page: 12
Definition2: \(\sum a^1_ia^2_i=0\)
Conjdef: Two orthogonal transformations \((\mathcal Z_i)_i\mapsto \sum a^j_i\mathcal Z_i\) such that