- Intuitive Visual Matrices Table of Contents TOC
- Math: Area of a Parallelogram equals geometric mean of triangles
- Math: Derivation of Matrix Determinant
- Two 2 dimensional determinant of a matrix animation showing it is equal to the area of the parallelogram
- Interpretation of Matrix determinant as hyper-volume
- Intuitive Matrix Inverse
- Solution of similtaneous linear equations
- Matrices, Eigenvalues, Eigenvectors
End of TOC
The 2 dimensional determinant of a matrix can be interpreted as the area of a parallelogram as shown in the following diagram.
Numeric Example
Compare that with the old fashioned area of two triangles that make up the parallelogram:
Using Pythagoras:
This carries on through higher dimensions. Below depicts a 3 variable system.
The rows r1, r2, r3 are vectors each. The various summations taken 1, 2 and 3 at a time define a parallelepiped.
The following excerpt is from X and may yield some insight when maximum entropy principle is applied. ( still working on this )
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