Introduction to Distributed Systems
14:36Distributed Systems 1.3: RPC (Remote Procedure Call)
19:44The Column Space of A Contains All Vectors Ax
52:14Multiplying and Factoring Matrices
48:25Orthonormal Columns in Q Give Q'Q = I
49:24Eigenvalues and Eigenvectors
48:55Distributed Systems 2.3: System models
20:44Positive Definite and Semidefinite Matrices
45:27Singular Value Decomposition (SVD)
53:33Broadcast Ordering
16:19Replication
25:21Distributed Systems 3.1: Physical time
20:47Consensus
18:15Raft
38:09Two-Phase Commit
18:45Linearizability
18:44Distributed Systems 3.2: Clock synchronisation
15:57Eventual Consistency
14:59Collaboration Software
36:26Distributed Systems: Google's Spanner
18:41Distributed Systems 3.3: Causality and happens-before
16:24Distributed Systems 4.1: Logical time
24:01Orthonormal Columns in Q Give Q'Q = I
MathWorks Professor of Mathematics
MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018.
This lecture focuses on orthogonal matrices and subspaces. Professor Strang reviews the four fundamental subspaces: column space C(A), row space C (A^T), nullspace N(A), left nullspace N (A^T).