Basis Vectors — Topic Summaries
AI-powered summaries of 4 videos about Basis Vectors.
4 summaries
No matches found.
Linear transformations and matrices | Chapter 3, Essence of linear algebra
Linear transformations in two dimensions are completely determined by where they send the two basis vectors, and matrices are just a compact way to...
Matrix multiplication as composition | Chapter 4, Essence of linear algebra
Matrix multiplication isn’t just a computational trick—it’s a compact way to represent composing linear transformations. A linear transformation is...
Three-dimensional linear transformations | Chapter 5, Essence of linear algebra
Linear transformations in three dimensions are fully determined by where they send the three standard basis vectors—so a 3D “grid-squishing” process...
Change of basis | Chapter 13, Essence of linear algebra
Coordinate systems aren’t just bookkeeping—they encode the geometry of space. In the standard setup, a vector like (3, 2) is interpreted as “3 units...