• The Mandarin (Chinese fusion): 1029 El Camino Real, Menlo Park, CA 94025
• The Kitchen (very classical cantonese): 279 El Camino Real, Millbrae, CA 94030
• Left Bank (sit down french): 635 Santa Cruz Ave, Menlo Park, CA 94025
• Jeffrey’s Hamburgers (chill, high quality American diner): 888 El Camino Real, Menlo Park, CA 94025
• Tai Pan (formal Chinese): 560 Waverley St, Palo Alto, CA 94301

a:2:{i:0;s:2:“f2”;i:1;s:2:“f3”;}

a:2:{i:0;s:2:“e2”;i:1;s:2:“e3”;}

a:2:{i:0;s:2:“e1”;i:1;s:2:“e2”;}

a:2:{i:0;s:2:“b2”;i:1;s:2:“b3”;}

a:2:{i:0;s:2:“c2”;i:1;s:2:“d8”;}

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