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Matrices are an extremely useful
and convenient way to
work with linear algebra.
We can rewrite linear
equations very
compactly with matrices.
And we can use matrices to set
up very general procedures for
solving such equations.
We're going to start here by
reminding ourselves what
linear equations are and how we
write them using matrices.
Then we will look at the general
way of solving linear
equations with matrices.
A key concept that helps us use
matrices in linear algebra
is the determinant.
We will remind ourselves
of this idea.
And how we can use it at
least for simple cases.
Finally, we're going to look
at the important idea of
eigenvalues and eigenvectors
with matrices.
The concept of eigenvalues and
eigenvectors is central to
quantum mechanics.
Essentially, the eigenvectors
will correspond to our ideas
of quantized states, and the
eigenvalues to the values of
quantities, such as energies,
associated with those states.
Understanding how those work
with matrix algebra is,
therefore, going
to be essential
and also very useful.
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