The Four Fundamental Subspaces: 4 Lines
... AV D A 4 v1 vr vn 5 D 4 u1 ur um 5 4 r 5 D U †: The v 0 s are orthonormal eigenvectors of AT A, with eigenvalue i2 0. Then the eigenvector matrix V diagonalizes AT A D .V †T U T /.U †V T / D V .†T †/V T . Similarly U diagonalizes AAT . When matrices are not symmetric or square, i ...
... AV D A 4 v1 vr vn 5 D 4 u1 ur um 5 4 r 5 D U †: The v 0 s are orthonormal eigenvectors of AT A, with eigenvalue i2 0. Then the eigenvector matrix V diagonalizes AT A D .V †T U T /.U †V T / D V .†T †/V T . Similarly U diagonalizes AAT . When matrices are not symmetric or square, i ...
