Orthogonal Projections (featuring U + U perp) 

Linear Algebra Pt.17
0:00 Orthogonal Complement (Perpendicular Subspace)
1:15 Projection onto a Subspace (decomposition into vector in U + vector in U perp)
2:41 Ex - Find orthogonal basis of U and vector in U closest to x
4:40 Ex - Write x as a sum of a vector in U and U perp
Linear Algebra Playlist: ru-vid.com/group/PLP_iTciEpA826mGQ8PotCPNkVEfY1KQGL
1. Vector Space Walkthrough & examples ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-XJ0h6bh_5Pw.html
2. Is it a Vector Space? (featuring crazy addition and multiplication rule) ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-RcjBbuRikMY.html
3. Extra Vector Space Properties & Proofs ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Qigr7sF9X7Y.html
4. Subspace Test Shortcut (and examples) ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-b50ys-uu33E.html
5. Span! Why is it the smallest subspace? When are 2 spans equal? ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-TjhLGIuXiac.html
6. Linearly Independent or Dependent? ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-pfrBHwGHUy0.html
7. Basis, Standard Basis, Dimension? (& finding multiple bases) ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-jQK_hE7nKQU.html
8. Carving & Enlarging Set to find a Basis (with the independent + dependent lemma) ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-W8axZxJSwFU.html
9. Row vs Column space of a matrix ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-9-besQN5tAg.html
10. What’s a LINEAR Transformation? Linear Operator? Matrix of a Transformation? ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-svAhfMxYSfs.html
11. Kernel, Image & Dimension of Transformations Explained! ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-mEsy0t5NbrM.html
12. Injectivity, Surjectivity & Bijectivity made easy ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-GELXmNO3ghg.html
13. Isomorphisms? Coordinate Isomorphisms? Proving linearity & bijection! ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-GELXmNO3ghg.html
14. Composition of linear transformations, Finding T INVERSE ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-L7g04DbI0V0.html
15.Orthogonality? Normalization? Expansion Theorem! ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-mmQyOD13zxs.html
16. Converting to an Orthogonal Basis! How “nice” ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-BoskFp4MitY.html
17. Orthogonal Projections (featuring U + U perp) ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-ZLDiXB255h4.html
18. Similar Matrices, Properties & Proofs ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-_nh7NBvLaD4.html
19. Diagonalization (And what actually are Eigenvalues, Eigenvectors and Eigenspaces?) ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-HGco-NMYozk.html
20. Showing Similarity when A~D and B~D ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-ziLfoAX1h1Y.html
21. Orthogonal Diagonalization ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-w_kJv1Kbp9A.html
22. Change of Basis (using coordinate isomorphism) ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-eD36KyC0z7E.html