- #1
Ahmad Kishki
- 159
- 13
Recommend a self study book for linear algebra with complex numbers
micromass said:I saw that you needed this for QM. In that case, everything you need to know is in this beautiful and excellent book: http://www.math.brown.edu/~treil/papers/LADW/LADW.html
You will find that LA over complex numbers is not very different from LA over the reals. But you'll see many topics in this book that are helpful for QM.
In linear algebra, real numbers are numbers that can be represented on a number line and have no imaginary component. Complex numbers, on the other hand, have both a real and imaginary component, and can be represented as a+bi, where a is the real part and bi is the imaginary part.
Complex numbers are used in linear algebra to represent vectors and matrices in higher dimensions. They are also used to solve systems of equations, perform rotations and transformations, and model real-world phenomena in engineering and physics.
One example of a complex number in linear algebra is the vector (3+2i, 1-4i, -2+3i). This vector has three elements, each with a real and imaginary component, and can be used in operations such as addition, subtraction, and multiplication.
The conjugate of a complex number a+bi is the number a-bi. In other words, the conjugate of a complex number has the same real part but the opposite sign of the imaginary part. In linear algebra, taking the conjugate of a complex number can be useful in operations such as finding the norm or magnitude of a vector.
To add complex numbers in linear algebra, you simply add the real and imaginary parts separately. For example, to add (3+2i) and (1-4i), you would do (3+1) + (2-4)i, which gives you 4-2i. To multiply complex numbers, you can use the FOIL method from algebra, but you also need to remember that i^2 = -1. For example, to multiply (3+2i) and (1-4i), you would do (3+2i)(1-4i) = 3-12i+2i-8i^2 = 11-10i.