Exam Prep Info  Part One
It is very important to know the "properties" of whatever we have defined in the course.
Examples are the properties of matrix operations: matrix inverse, matrix transpose,
matrix addition, matrix multiplication, and the multiplication of a matrix by a scalar.
Other examples are the properties of the dot product and the properties above that
become "axioms" for the inner product space and the vector space.
For the dot product, know both the Real number version & the Complex number
version. Be prepared for "unusual, nonstandard" definitions of scalar multiplication,
vector addition, and especially the inner product of vectors. We tested you on the
midterm with such unorthodox definitions and you can expect to be so tested again. As
you know, if these definitions satisfy the axioms we do have a vector space or possibly
an inner product space. If the axioms are not all satisfied, we don't.
Make sure you understand linear transformations, and in particular what makes a
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 Spring '08
 All
 Math, Linear Algebra, Addition, Multiplication, Matrix Operations, Vector Space, inner product

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