
Linear Algebra Done Wrong [pdf] - TriinT
http://www.math.brown.edu/~treil/papers/LADW/LADW.pdf
======
aconbere
While not explicitly mentioned in the introduction I think it's safe to say
that the books title is a play off of the popular title "Linear algebra done
right"

[http://www.amazon.com/Linear-Algebra-Right-Sheldon-
Axler/dp/...](http://www.amazon.com/Linear-Algebra-Right-Sheldon-
Axler/dp/0387982582/ref=sr_1_1?ie=UTF8&s=books&qid=1260994052&sr=8-1)

Which is a pretty amazing text if you're delving in to the algebra side of
linear algebra. Though I suspect significantly less useful than "Linear
algebra done wrong".

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klodolph
Looks suspiciously like the professor's notes from the linear algebra class I
took (on the opposite side of the same country) for the first part. Then my
professor started talking about homomorphisms, and things started getting
GOOD.

A vector space is an abelian group, a scalar field, and a homomorphism from
the field to automorphisms of the group. That's all you need to remember for
definitions.

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antimora
Curious: has any of you used Linear Algebra in outside settings of academia? I
know there are lots of uses in stats, numerical analysis, non-linear dynamics,
and optimization but I've never used it practically.

~~~
hyperbovine
Yes. It's huge in engineering, for example:
[http://commons.bcit.ca/math/examples/civil/linear_algebra/in...](http://commons.bcit.ca/math/examples/civil/linear_algebra/index.html)

According to one of my linear algebra professors from back when, a lot of
computational linear algebra was developed by the Soviets in the mid-20th
century as a way to carry out optimized central planning. So I guess another
application would be, socialism.

No idea if this is true or not but it's a good story. Also goes a long way
towards explaining why so many linear algebra textbooks are translated from
Russian.

~~~
TriinT
_"Also goes a long way towards explaining why so many linear algebra textbooks
are translated from Russian."_

I think you're detecting a false pattern there. Russians generally do kick ass
in Mathematics. In the West, Mathematics was held back by the Bourbaki
fanatics, while in Russia they were never afraid of marrying the pure with the
applied, the beautiful with the useful.

There may be a lot of Linear Algebra books translated from Russian, but there
are also a lot of other books by Arnold, Kolmogorov, Fomin, Gelfand, etc that
were also translated from Russian and that were not on Linear Algebra.

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Dilpil
I am always amazed at textbooks that introduce axioms and then later (or
never!) show why they are interesting. Do any mathematicians actually think in
this way?

~~~
vitaminj
To me, one of the interesting things about how mathematical results have been
discovered historically is that they have often been accidental (or intended
for something else).

eg. eigenvalues were originally looked at for use with quadratic forms, but
people later found that its interesting properties (orthogonality, symmetry,
etc) were useful for lots of other things.

There is often also a large gap in time between when a mathematician playing
around with a problem discovers an interesting result and when it is actually
applied to something useful.

eg. Euler's law regarding complex exponentials was developed around 1740, but
it wasn't until around 1807 when Fourier used it in harmonic analysis and 1897
when Steinmetz started applying it to electrical engineering.

But you wouldn't know that from reading a textbook, which is (understandably)
arranged in such a way that omits historical context and why people bothered
to study it in the first place. Most linear algebra books are classic examples
of how to introduce abstract topics without any context.

