determinant and volume
(1.1 hours to learn)
Summary
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.
Context
This concept has the prerequisites:
Core resources (read/watch one of the following)
-Free-
→ 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.
-Paid-
→ 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
See also
-No Additional Notes-