determinant and volume
(1.1 hours to learn)
The volume of a box in n dimensions is given by the determinant of the matrix whose columns are the sides of the box. When a matrix is used as a linear transformation, it scales the volume of a set by its determinant.
This concept has the prerequisites:
Core resources (read/watch one of the following)
→ Khan Academy: Linear Algebra
- Lecture "Determinant and area of a parallelogram"
- Lecture "Determinant as scaling factor"
→ MIT Open Courseware: Linear Algebra (2011)
Videos for an introductory linear algebra course focusing on numerical methods.
→ Introduction to Linear Algebra
An introductory linear algebra textbook with an emphasis on numerical methods.
Location: Section 5.3, "Cramer's rule, inverses, and volumes," subsection "Area of a triangle," pages 271-274
-No Additional Notes-
- create concept: shift + click on graph
- change concept title: shift + click on existing concept
- link together concepts: shift + click drag from one concept to another
- remove concept from graph: click on concept then press delete/backspace
- add associated content to concept: click the small circle that appears on the node when hovering over it
- other actions: use the icons in the upper right corner to optimize the graph placement, preview the graph, or download a json representation