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Sorry, I know i m asking dumb questions but i just want to understand more Since $x^t Ax=\langle x, Ax\rangle$ (the inner product), the question may be stated: Is there a transformation that maps every vector to something orthogonal to itself?What should come to mind is a rotation matrix that rotates $\mathbb^2$ by 90 degrees, which Shu Xiao Li has presented.This shield decays slowly if you haven't dealt or taken damage in the last 25 seconds. Dealing physical damage grants 20 movement speed for 2 seconds.Your Energized attacks gain 35% bonus Range ( 150 range maximum) and deal 50~120 bonus magic damage (based on level) on hit. Assists on Cleaved enemy champions or kills on any unit grant 60 movement speed for 2 seconds instead.You added an extra term before the $...$ and multiplied it by $x$.Then you added another term after the $...$ and multiplied it by $(-y)$. It should be possible to prove this using the basic properties of numbers discussed in Spivak's book: Associative law for addition, Existence of an additive identify, Existence of additive inverses, Commutative law for addition, Associative law for multiplication, Existence of a multiplicative identity, Existence of multiplicative inverses, Commutative law for multiplication, and Distributive law.
This could have been better explained, although I see what you did now.(cheifly British)In the UK, ' X' is commonly used at the end of a message to represent kisses.