Matrices, Determinants, and the Birth of Linear Algebra - A Historical Perspective

Explore the historical development of matrices, determinants, and linear algebra in this comprehensive math history lecture. Trace the origins of solving systems of equations from ancient Chinese mathematics to the contributions of influential mathematicians like Leibniz, Cramer, Laplace, Vandermonde, Cauchy, Cayley, and Sylvester. Examine key concepts such as Cramer's Rule, Laplace's expansion of determinants, and Euler and Bezout's work on resultants. Discover how Sylvester reformulated these polynomials as determinants, shaping the foundations of modern linear algebra. Gain valuable insights into the evolution of mathematical thinking and the interconnected nature of algebraic concepts throughout history.