Linear Algebra and Quantum Mechanics Crash Course (50 pts.)

Mathematics and Linear Algebra Overview

In the programming language of your choice, define the following variables and complete the following calculations. You may use built-in functions (such at the Numpy library) or create your own functions. Verify that your answers are correct either by hand or using an online linear algebra solver such as Wolfram Alpha.

  1. (8pts.) Define two real scalars (a and b) and give them any valid values. Compute the addition, subtraction, multiplication, and division of a and b.
  2. (10 pts.) Define two imaginary scalars (c and d) and give them any valid values. Compute the addition, subtraction, and multiplication of c and d. Also compute the modulus of c and the modulus squared of d.
  3. (16 pts.) Define two vectors (e and f) of length 3. The elements can be real or imaginary. Compute the addition, subtraction, dot product, and cross product of e and f. Find the magnitude of e and the unit vector of f.
  4. (16 pts.) Define two 2x2 matrices (A and B). The elements can be real or imaginary. Compute AB, BA, the commutator of A and B, and the addition and subtraction of A and B. Compute the transpose and inverse of A, the complex conjugate of B, and the adjoint of A.