*A New Way to Start Linear Algebra*. The key point is to start right in with the columns of a matrix

*A*and the …

These brief videos, recorded in 2020, contain ideas and suggestions from Professor Strang about the recommended order of topics in teaching and learning linear algebra. The first topic is called *A New Way to Start Linear Algebra*. The key point is to start right in with the columns of a matrix *A* and the multiplication *Ax* that combines those columns.

That leads to *The Column Space of a Matrix* and the idea of independent columns and the factorization *A = CR* that tells so much about *A*. With good numbers, every student can see dependent columns.

The remaining videos outline very briefly the full course: *The Big Picture of Linear Algebra*; *Orthogonal Vectors*; *Eigenvalues & Eigenvectors*; and *Singular Values & Singular Vectors*. Singular values have become so important and they come directly from the eigenvalues of *A’A*.

A new video recorded in 2021, *Finding the Nullspace: Solving Ax = 0 by Elimination*, computes the nullspace of any matrix *A*.

You can see this new idea developing in the first video lecture of Professor Strang’s 2019 course *18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning*.

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