In this lecture, viewers learn about what it means for vectors and subspaces to be orthogonal. The instructor begins by explaining what it means for vectors to be orthogonal, and then extends the definition to subspaces. He shows that the row space is orthogonal to the null space, and explains how this fact is useful in cutting the whole space up into two perpendicular subspaces. The lecture is informative and engaging, and provides a clear understanding of orthogonal vectors and subspaces.
Orthogonal Vectors and Subspaces -- Lecture 14. Learn what it means for vectors and subspaces (and even bases) to be orthogonal.
Gilbert Strang, 18.06 Linear Algebra, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 22, 2008). License: Creative Commons BY-NC-SA.
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Questions answered by this video:
What are orthogonal vectors?
What does it mean for vectors and subspaces to be orthogonal?
How can you tell if two vectors are orthogonal?
How can you tell if two subspaces are orthogonal?
Why is the row space orthogonal to the nullspace?
What are orthogonal complements?
Currently 4.0/5 Stars.
This video is a very complete and in-depth discussion of orthogonality and what it means for vectors and subspaces to be orthogonal. A very understandable and great explanation of orthogonal spaces.