This is just a collections of specific terms in linear algebra and matrix computations. Instead of providing the calculation function, it just provides a direct view to explain these terms.
span: The “span” of \(\vec v\) and \(\vec w\) is the set of all the linear combinations.
where \(a\) and \(b\) vary over all real numbers.
linear transformation: compositions of “rotation” and “shear” operation. Applying one transformation after another.
Determinant: to measure the fact of by which the given region increase or decreases.
- \(det(M)=0\) mean it squash the matrix into lower dimension.
- negative determinant: flip over the orientation of your axes.