UNSW Study Map — courses, mapped like a game

Family 4

Orthogonality: GS / QR / complement

These 3 topics share one solution. Spot the family, apply the method — same trick, different story.

Orthogonal complement basis："find a basis for the orthogonal complement" · 平面方程给 $U$ 求 $U^\perp$ ;或 span 给 $W$ 求 $W^\perp$
QR factorisation & image complement："Find a QR factorisation of the 5×2 matrix A" · (b) 挑出不在 $\operatorname{im}(A)^\perp$ 里的向量
Gram–Schmidt orthonormalisation："find an orthonormal basis for W = span{x1, x2}" · $\mathbb{R}^4$ 里两个向量正交化

The concepts behind this family's method — brush up first if unsure.

orthogonal complement, Gram–Schmidt, projection