OMG its Gram-Schmidtting!!! Ok so like orthonormal basis are so nice, don’t you want to make them out of boring-ass normal basis? Of course you do.

Suppose \(v_1, … v_{m}\) is a linearly independent list in \(V\). Now let us define some \(e_{1} … e_{m}\) using the procedure below such that \(e_{j}\) are orthonormal and, importantly:

\begin{equation} span(v_1, \dots, v_{m}) = span(e_{1}, \dots, e_{m}) \end{equation}

The Procedure

We do this process inductively. Let:

\begin{equation} e_1 = \frac{v_1}{\|v_1\|} \end{equation}

A grammar is a set of logical rules that form a language. (more precisely defined in goals of a grammar)

goals of a grammar

• explain natural languages in syntax + semantics
• have described algebras which can be used to evolve the syntax
• …that describe the grammatical operations

The formalism here is that a rigorous grammar should have:

1. semantic accountability
2. generativity

Recall the definition of graph : if you can relabel \(G\) to get \(G’\), that they are the same up to relabling.

Using constructor theory to test whether or not gravity in quantum theory is just entanglement.

This solves problem with gravity.