Essence of Linear Algebra
3Blue1Brown
Fifteen short videos that give you geometric intuition for vectors, matrices, linear transformations and eigenvectors. Watch this before any quantum math and everything afterwards is easier.
Beginner · 6 resources
Math prerequisites
To go past intuition you need complex numbers, vectors, matrices, inner products and eigenvectors. That is roughly one solid linear algebra course — not a physics degree.
Why it matters
This is the wall most self-taught learners hit. Front-loading a few weeks of linear algebra makes the intermediate level dramatically easier and is the highest-leverage thing a beginner can do.
After this you will be able to
- Multiply matrices and vectors comfortably
- Work with complex numbers, conjugates and the modulus squared
- Understand eigenvectors, unitary matrices and tensor products
Start here
3 best places to start
Hand-picked and ordered. If you only have time for one, take the first.
18.06 Linear Algebra
MIT OpenCourseWare (Gilbert Strang)
Strang's legendary course, with full video lectures, problem sets and exams. This is the deep version of the prerequisite — do it if you want real fluency rather than a passing acquaintance.
Linear Algebra
Khan Academy
Exercise-driven and self-paced, with instant feedback. The best option if you want to practise mechanics — matrix multiplication, eigenvectors — until they are automatic.
Also covering this
3 more resources
8.04 Quantum Physics I
MIT OpenCourseWare (Barton Zwiebach)
Optional but clarifying. Quantum computing does not require a physics course, but if you want to know where the postulates come from rather than accepting them, start here.
Quantum states are complex vectors and gates are matrices, which in Python means NumPy arrays. This short guide covers everything you need, including complex dtypes.
Quantum Computing Stack Exchange
Stack Exchange
Where to ask when you are stuck, and often where your question has already been answered by a working researcher. Search before posting — the back catalogue is deep.
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Topics that list Math prerequisites as a prerequisite.