Explore quantum linear algebra algorithms for machine learning in this comprehensive lecture from the Quantum Colloquium series. Delve into quantum singular value transformation (QSVT), a unifying framework developed by Gilyén et al., and its applications in achieving quantum speedups for machine learning problems. Examine the typical structure of such applications, barriers to super-polynomial quantum speedup, and current literature addressing these challenges. Discover the intriguing connection between quantum linear algebra and classical sampling and sketching algorithms through "quantum-inspired" classical algorithms. Cover topics including blocking coding, linear algebra on quantum states, linear combinations, literary polynomials, Lipschitz matrix functions, block encoding, and sample query axis. Gain insights into the input and output problems, sample data structures, and composition properties in this in-depth exploration of quantum linear algebra's potential in advancing machine learning techniques. Read more