Linear Algebra · Advanced · 11 min
Orthogonality
Orthogonal decomposition splits a vector into independent perpendicular contributions.
WHAT HAPPENS IF…For u=(3,0,0), what is the parallel part?
Loading the mathematical model…
With n=(1,2,2), n·n=9. The parallel part is [(u·n)/9]n and the remainder has dot product zero with n. The components are orthogonal, so their squared lengths add to ||u||². The displayed plane represents all vectors perpendicular to n.
A detail that matters
Zero is orthogonal to every vector but has no direction.
Keep the connection going
More linear algebra ↗