Mathematics Linear Algebra Quotes

Mathematics is the science which draws necessary conclusions.

Matrices act. They don't just sit there.

The contribution of mathematics, and of people, is not computation but intelligence.

The reason special names are given to these quadratic irrationalities is that any quadratic algebraic integer is a linear combination (with ordinary integers as coefficients) of 1 and one of these fundamental quadratic algebraic integers.

The collection of all real or complex numbers that are integral linear combinations of 1 and τd is closed under addition, subtraction, and multiplication, and is therefore a ring, which we denote by Rd. That is, Rd is the set of all numbers of the form a + bτd where a and b are ordinary integers. These rings Rd are our first, basic, examples of rings of algebraic integers beyond that prototype, , and they are the most important rings that are receptacles for quadratic irrationalities. Every quadratic irrational algebraic integer is contained in exactly one Rd.

It is simpler to redefine the meaning of “equal.

You cannot read mathematics the way you read a novel. If you zip through a page in less than an hour, you are probably going too fast.

You cannot read mathematics the way you read a novel. If you zip through a page in less than an hour, you are probably going too fast.