Numerical Algebra

My blog about my learning of Numerical Linear Algebra.

Why Learn this?

In real life we use computers to calculate math, solve equations, plot functions, and with this you run algorithms in any field. For example in computer vision you are executing edge detection algorithms and then used to indentify objects in a scene (really basic perception of the world) or you are training a neural network with million of parameters example , large language models, meaning that you are adjusting each of them for each iteration for finding the best set of parameters that minimize the loss function. All of this involve matrix multiplications and linear algebra operations. For me is really important to make it fast and efficient, and this is what numerical linear algebra is all about, due to my high interest in make this system understand their environment and make decision based on it in and efficent way, efficent its about time and memory. But also linear algebra itself is facinating, is one of the most powerful tools that we have to solve problems, undestanding what are vectors and transformation of them is the key to understand many other conepts.

Course references

I am following the open source course “Introductio to Numerical Methods” by Prof. Steven G. Johnson at MIT.

References

I am using the following books as primary references:

• Numerical Linear Algebra (Trefethen & Bau)
• Fundamentals of Matrix Computations (Watkins)