Question 1: Such spontaneous symmetry breaking has found further application in elementary particle physics, where its occurrence is related to the appearance of ________.

Question 3: A standard example is the general linear group introduced above: it is an ________ of the space of all n-by-n matrices, because it is given by the inequality

Question 10: Expressed in words, adding a to b first, and then adding the result to c gives the same final result as adding a to the sum of b and c, a property known as ________.