Most of this will be completely incomprehensible if you aren’t mathematically trained.\u00a0 I’m putting it out there anyway.<\/p>\n
Thou shalt not confuse a vector space with its dual.\u00a0 Thou shalt not add unnecessary structure without good cause.\u00a0 Be careful not to identify objects related by noncanonical isomorphisms.\u00a0 When composing isomorphisms, bear in mind the possibility of a “twist” when thou comest back to the same object again.<\/p>\n
Do not favor subspaces over quotient spaces, nor quotient spaces over subspaces, but give equal justice to all methods of reduction.<\/p>\n
Never be unjust to a mathematical entity, lest it rise up against you.\u00a0 When something is taken away from a system, it is often needful to add something as well, to compensate it and to preserve its integrity.<\/p>\n
Study a nonlinear thing by passing to a bigger linear algebra.<\/p>\n
0 is a natural number.\u00a0 Always include the identity, or the empty object, when you allow more than one of a thing.\u00a0 Almost everything there can be two of, there can also be zero of.\u00a0 But, if thou allowst only 1 of a thing, do not consider 0 to be a special case!\u00a0 This rule of “0” holds in additive contexts; in multiplicative contexts “1” is nothing.<\/p>\n