Linear algebra has been a crucial part of my learning journey, especially as I ventured into quantum computing. I started with Gilbert Strang's Introduction to Linear Algebra to build a strong foundation, but I often found myself exploring much deeper concepts and proofs beyond what the book covered. Throughout this process, Mathematics Stack Exchange became an invaluable resource for clarifying doubts, solving challenging problems, and learning through engaging discussions with the community.

These notes are an attempt to organize and share what I’ve learned over the years. They reflect not only the material from Strang's book but also the extended explorations and insights I’ve gained while tackling questions and problems. Having enrolled in Math 6108 Applied Matrix Theory at Missouri S & T, my notes go well beyond the scope of a 6000-level advanced graduate course.