Orthogonal Memes

Linear algebra students everywhere are triggered by this classic mathematical troll move. The equation shows y = (y·u₁/u₁·u₁)u₁ + (y·u₂/u₂·u₂)u₂ where those fractions are screaming to be simplified. But textbook authors refuse to cancel the u's because they're not actually the same term - one is a dot product in the numerator and another is in the denominator. It's like thinking you can cancel the 2's in 2+3/2+5. You can't! Math professors secretly giggle every time a student makes this mistake and then has to sheepishly erase their work. The projection formula may look tempting, but those u's are staying right where they are!

The real reason Neo took the red pill? Morpheus was secretly a linear algebra enthusiast. Instead of showing humans trapped in gooey pods, he just bored them to death with QR decomposition lectures. The Gram-Schmidt process isn't just orthogonalizing vectors—it's apparently the ultimate weapon against human consciousness! No need for robot overlords when you can simply inflict matrix factorization on unsuspecting victims. The true horror of The Matrix wasn't the machines harvesting humans for energy—it was forcing them to sit through linear algebra finals without coffee.

Regular folks: "Those lines are perpendicular." Mathematicians in formal attire: "I believe you mean orthogonal , my good sir." *adjusts monocle* It's the same exact thing—two lines meeting at 90° angles—but mathematicians just can't resist using the fancy term that makes calculus students cry themselves to sleep. Classic academic flexing!