There are ten thousand examples I want to give of why you're wrong. We have to start somewhere so here's a favourite, the "universal projection formula":
(A.B)/B
Projects any A onto any B, in any number of dimensions and with any signature (eg hyperbolic/Euclidean/elliptic). A and B can be lines, planes, points, and with a conformal or anti de Sitter metric a sphere or hyperboloid etc ("blades").
It works because A.B is dimension independently the object "orthogonal to A and containing B or vice versa". And division by B will intersect that orthogonal object with B.
Concise, intuitive, and powerful. What's the linear algebra formula you'd consider to be comparable?
(A.B)/B
Projects any A onto any B, in any number of dimensions and with any signature (eg hyperbolic/Euclidean/elliptic). A and B can be lines, planes, points, and with a conformal or anti de Sitter metric a sphere or hyperboloid etc ("blades").
It works because A.B is dimension independently the object "orthogonal to A and containing B or vice versa". And division by B will intersect that orthogonal object with B.
Concise, intuitive, and powerful. What's the linear algebra formula you'd consider to be comparable?