Math 307 Exam 2 Review

The second midterm will be held in class on Friday, April 1 (really). It will be a closed-book, closed-notes exam, and will cover all material covered in class through Wednesday, March 30. This includes in particular all of chapters 1 - 6 and at least the first two sections of chapter 7 of the textbook.

You will be asked for complete definitions (including appropriate context, e.g., what kind of thing might be linearly independent?) of some subset of the following terms. This includes all the terms from the first exam, plus new ones from the material covered since then. Remember that a complete mathematical definition leaves no room for ambiguity: if you give me a definition of what it means for a list of vectors to be linearly independent, I need to be able to use it, in principle anyway, to decide whether or not any list of vectors I ever meet is linearly independent.

vector space
subspace
direct sum
linear combination
span
finite dimensional
linearly independent
basis
standard basis
dimension
linear map
null space
range
injective
surjective
matrix of a linear map
invertible
isomorphism
invariant subspace
eigenvalue
eigenvector
upper triangular
diagonalizable
norm
inner product
orthogonal
orthonormal
orthogonal complement
orthogonal projection
linear functional
adjoint
self-adjoint
normal

In lieu of review problems, I advise you primarily to study the homework problems. Do them again from scratch, compare your solutions to the ones I handed out in class, then do them again a few days later. For more preparation, start on other problems from the book.

Also, I suggest reading this article about study habits.

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