This is the solution to the first problem of the first section of Quantum Mechanics for the work professional. You can find the details and notes here:
https://pasayten.org/quantum-mechanic...
We delve a little deeper into the basic matrix and vector arithmetic you'll need throughout this course, talking about the transpose of not only vectors but also matrices, and explain the need for both row and column vectors. We also talk about how the transpose works on multiple objects at once, and what the relationship is between vectors, matrices, their deals and the inner product.
The course itself has a website here:
https://pasayten.org/quantum-mechanic...