Math 55a: Honors Abstract Algebra
Homework Assignment #7 (18 October 2010):
Linear Algebra VII: The spectral theorem; spectral graph theory; symplectic structures
It is my experience that proofs involving matrices can be shortened by 50% if one throws the
Math 55a: Honors Abstract Algebra
Homework Assignment #1 (1 September 2010):
Linear algebra I: vector space basics; introduction to convolution rings
Axler, page 1 [why?]
*
This problem set is due Friday, September 10, at the beginning of class.
We start
Math 55a: Honors Abstract Algebra
Homework Assignment #4 (24 September 2010):
Linear Algebra IV Eigenstu
(and a projective overture)
HINT, n.: The hardest of several possible ways to do a proof.1
For a vector space V over a eld F , the projective space PV
Math 55a: Honors Abstract Algebra
Homework Assignment #5 (1 October 2010):
Linear Algebra V: tensors, more eigenstu, and a bit on inner products
The terms proper value, characteristic value, secular value, and latentvalue or latent root are sometimes used
Math 55a: Honors Abstract Algebra
Homework Assignment #2 (10 September 2010):
Linear Algebra II
TFAE (The Following Are Equivalent): If I say this it means that, and if I
say that it means the other thing, and if I say the other thing. . . 1
This homework
Math 55a: Honors Abstract Algebra
Homework Assignment #6 (8 October 2010):
Linear Algebra VI
to ne tol ko otricatel na veliqina, no otricatel na veliqina vozvedenna v kvadrat!1
Some more results about bilinear pairings and inner products:
1. [Strange life
Math 55a: Honors Abstract Algebra
Homework Assignment #9 (1 November 2010):
Linear Algebra IX: Exterior algebra and determinants, contd
*, 231 Symbol Index on p.247
Axler,
The symbols
that appear on the rst page of these chapters are decorations
[. . . ]
Math 55a: Honors Abstract Algebra
Homework Assignment #11 (29 November 2010):
Representations of nite groups
i2 = j 2 = k 2 = ijk = 1
W.R. Hamilton, 1843 [cut into a stone on Brougham1 Bridge, Dublin; see also the
nal two problems].
We start with some app
Math 55a: Honors Abstract Algebra
Homework Assignment #10 (10 November 2010):
Linear Algebra X:
Signatures and real polynomials; determinants and distances; Pontrjagin duality0
Quotes? We dont need no stinkin quotes!
adapted or misquoted from Blazing Sadd
Math 55a: Honors Abstract Algebra
Homework Assignment #8 (25 October 2010):
Linear Algebra VIII:
As soon as I get into [Math 55] class, Im ghting o a swarm
Of positive-denite non-degenerate symmetric bilinear forms!
from a somewhat redundantly titled patt
Math 55a: Honors Abstract Algebra
Homework Assignment #3 (17 September 2010):
Linear Algebra III
The expression ij [see problem 8] is called the Kronecker delta (after the
mathematician Leopold Kronecker [18231891], who made more substantial contributions