What is a line integral?

Questions:
Vectors, Matrices and Vector Calculus:

1. How are vectors and matrices related?
2. Can matrices move vectors around? If yes, how?
3. What dimensions do cross products exist on?
4. What is an Eigen vector? Why is it special?
5. Give an example of a vector space of 3 dimensions.
6. What dimensions does a M2x2 () have? Give an example.
7. Why do we need to diagonalize a matrix?
8. What is the Gram-Schmitt Process?
9. What is a vector field?
10. What is a conservative vector field?

Complex Analysis:

1. What is a partial derivative?
2. What is a directional derivative?
3. What is a line integral?
4. What are double integrals?
5. What is a counter integral?
6. What is a complex number?

7. Explain Greens Theorem, Stokes Theorem.

1. What is 3, where ?

1. What is of ?

1. What is ?

1. What are Cauchy-Riemann equations?

1. What is ?