Curious About Science

I'm 𝙞𝙢𝙢𝙚𝙣𝙨𝙚𝙡𝙮 curious. To me everything we learn is just a small piece to an enormous puzzle that we are diligently working to construct. As the connection between these pieces becomes clear, and the lightbulb moment happens, the excitement that ensues is simply boundless! I can't help myself but to nerd-out and share!

Science is a phenomenal exploration of nature. We hope to hone our skills of problem solving by exposing ourselves to multiple contexts. In doing so, it can sometimes be challenging to see the connection between topics. I yearn to understand 𝙝𝙤𝙬 these aspects of physics, unite together. To accomplish this, I'll cover all of my old textbooks through QFT; the convergence point of the many modern scientists! These posts are very much in a "𝘯𝘰𝘵𝘦𝘴 𝘵𝘰 𝘴𝘦𝘭𝘧" style. 𝙈𝙮 𝙝𝙤𝙥𝙚 is that by sharing this exploration, I can help others navigate the beautiful world of mathematics & physics through problems and examples, connecting the mathematical tools to their physical ramifications.

Understanding the Dot Product: Geometric vs. Algebraic Definitions ⇢ 1.7 from Classical Mechanics

Understanding Vector Orthogonality with Dot Products! ⇢ 1.6 from Classical Mechanics

Geometry of the Dot Product: Angle Between Cube Diagonals Explained! ⇢ 1.5 from Classical Mechanics

Master 3D Vectors: From Pythagoras to Vector Angles ⇢ 1.3 & 1.4 from Classical Mechanics

Problem A.31 - Diagonalize Your Expectations ⇢ The Matrix Exponential Journey: Intro to QM Appendix

Problem A.30 - Unitary Operators ⇢ The Quantum Mechanics Powerhouse: Intro to QM Appendix

Problem A.29 - Diagonalizing Matrices with Degenerate Eigenvalues ⇢ Gram-Schmidt in Action: Appendix

Problem A.28 - Similarity Invariants ⇢ Hidden Beauty of Matrix Diagonalization: Intro to QM Appendix

Problem A.27 - Hermitian Transformations in Quantum Mechanics ⇢ A Sketch Proof: Intro to QM Appendix

Problem A.26 - Simultaneous Diagonalization with Degenerate Eigenvalues: Intro to QM Appendix

Problem A.25 - Matrix Harmony ⇢ Two Matrices, One Set of Eigenvectors: Intro to QM Appendix

Problem A.24- Eigenvector Invariance in Simultaneously Diagonalizable Matrices: Intro to QM Appendix

Problem A.23- Immortal Property⇢ Commutativity in Normal Matrices Across Basis: Intro to QM Appendix

Problem A.22 - Matrix Rebellion ⇢ When Non-Normal Meets Diagonalizable: Intro to QM Appendix

Problem A.21 - Eigenvalue Symphony ⇢ Orchestrating Traces and Determinants: Intro to QM Appendix

Problem A.20 - Cracking the Matrix Code ⇢ Unveiling Characteristic Polynomials: Intro to QM Appendix

Problem A.19 - The Curious Case of Non-Diagonalizable Matrices: Intro to QM Appendix

Problem A.18 - Exploring the Eigen landscape ⇢ Eigenvalues and Eigenvectors: Intro to QM Appendix

Problem A.17 - Matrix Traces Unveiled ⇢ When Mathematical Rules Break Down: Intro to QM Appendix

Problem A.16 - Matrix Transformations ⇢ Similarity, Hermiticity, and Unitary: Intro to QM Appendix

Problem A.15-Symmetry in Motion⇢ The Elegant Algebra of Rotation Transformations: Intro to QM Append

Problem A.14- Geometric Transformations⇢ Rotation Matrices & Direction Cosines: Intro to QM Appendix

Master Vector Operations: From Basic Addition to Cross Products ⇢ 1.1 & 1.2 from Classical Mechanics

Problem A.13- Determinants of Special Matrices⇢ Hermitian, Unitary, Orthogonal: Intro to QM Appendix

Problem A.12 - Unitary Matrices ⇢ The Orthonormal Comedy Club: Intro to QM Appendix

Problem A.11 - Matrix Alchemy ⇢ The Secret Life of Matrix Products and Sums: Intro to QM Appendix

Problem A.10 - Matrix Metamorphosis ⇢ Unveiling the Hidden Forms Within Every Matrix: Intro to QM

Problem A.9 - The Product Tango ⇢ When Vectors and Matrices Collide: Intro to QM Appendix

Problem A.8 - Matrix Mastery ⇢ Basic Matrix Operations Unveiled: Intro to QM Appendix

Problem A.7 - Vector Algebra's Hidden Boundary ⇢ The Triangle Inequality: Intro to QM Appendix