Horn wrote about my work,
"Best performance in the course
throughout the semester. Knows
this material cold."

It was just true. Why? It was
an 'advanced' course in linear
algebra and matrix theory, and I'd
never had even a first course in the subject.

But long before the course, in total
I'd done much more than just such a
course.

I had had two good courses in
abstract algebra, each of which had
provided a good foundation for linear
algebra and also touched on the
subject.
I had taken a
reading course in theoretical physics
based heavily on matrix theory.
And I had written my undergraduate honors
paper on group representation theory,
essentially in linear algebra.

I'd worked carefully through
two of the best books on linear algebra,
one by E. Nearing and the other by P.
Halmos. The Halmos book is famous as
the crown jewel of books on linear
algebra. Why? It can be good to look
at linear algebra as a baby version of
Hilbert space theory, heavily from
von Neumann, and Halmos wrote his book
when he was an assistant to von Neumann
at the Institute for Advanced Study.
So, deliberately, the Halmos book is
an introduction to Hilbert space theory.
It also has the profound perspective
of one of the best mathematicians of
all time and the elegance of thought
of von Neumann.

For applications, in my career and in
my own study, I'd worked through stacks
of books and papers on applications
in numerical linear algebra, multivariate
statistics, optimization, curve fitting,
signal processing, especially around
the fast Fourier transform, differential
equations, advanced calculus, deterministic
optimal control theory, exterior algebra, etc.

At one point I wrote my own notes on much
of linear algebra, with black ink on
white paper, 100% cotton I got especially
for the notes. My work was very careful
although not elegant.

For review, just before the course, I wrote
out from memory 80 pages covering about
2/3rds of the course. As Horn wrote, I
knew the subject cold, long before I took
his course. Horn's homework, tests, and
final exam were all challenging for the
other students, and I effortlessly blew
them away, by large margins on all three.
E.g., I never studied for the tests or
either the mid-term or final exam. When
doing the homework, I nearly never looked
at my notes from class and, instead, just
wrote out the solutions based on what
I already knew.

I didn't belong in the course and had told
the department that at the beginning. The
department's reaction was to smile and
say "Take the course anyway.". So, I did.

For me, the course was a huge waste:
From a long commute to campus and taking
care of my wife, I was short on time, but
the Horn homework had me
up nearly all night and then exhausted
the next day once a week and, thus, ate
into a big fraction of the best time I
had each week. Some of my other, more
important work suffered. When I did
the Horn homework, I was usually just
exhausted. I'd get the papers back,
graded, in about two weeks, recognize
my handwriting, but, from having been
so tired, actually had no memory of
having done the work. Bummer. It was
a trial by fire and exhaustion, not
education. I was being asked to
'prove myself', not learn something.

In the program, I only wanted to learn
some good material and had no desire
at all to 'compete', certainly not in
that linear algebra course beneath me.
I didn't know I was blowing away the
other students until the grader showed
me the scores on homework and tests,
all except the final exam.

In many ways Horn was a very good teacher,
but, in total, he blew away nearly all the
students. If I hadn't already known the
material coming into the course, then I
couldn't have learned it in the course.
The way I had learned the material was
from some slow, careful, thoughtful study
and a lot of work with applications,
and the course offered neither.