I also love this series of lectures, but in this lecture I find that he does not explain perpendicular subspaces enough. The example with the blackboard and the floor is just confusing (to me and my colleagues at least), because obviously they form a right angle and thus are perpendicular. And obviously they are both subspaces. Which leads me to believe that the definition is wrong, which I'm sure it isn't.####[['lecture', 'Course_General_Feedback', 'NEG'], ['perpendicular subspaces', 'Mathematical_Related_Concept', 'NEG'], ['example', 'Teaching_Setup', 'NEU'], ['series of lectures', 'Teaching_Setup', 'POS'], ['NULL', 'Instructor', 'NEG'], ['blackboard', 'Teaching_Setup', 'NEU'], ['right angle', 'Mathematical_Related_Concept', 'NEU'], ['perpendicular', 'Mathematical_Related_Concept', 'NEU'], ['subspaces', 'Mathematical_Related_Concept', 'NEU']]