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Summary: Things You Should Know (from Linear Algebra)
Jonathan Harel
April 11, 2009
Contents
1 Spaces 1
2 Eigenvalues and Eigenvectors 1
2.1 Diagonalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
3 Singular Value Decomposition (SVD) 3
4 Symmetric Matrices 3
5 Positive De...nite Matrices 4
6 Principal Component Analysis (PCA) 5
1 Spaces
Matrices have dim(row-space) = dim(col-space). For example, a random 2x60
matrix has a row-space spanning a planar subspace in R60
(with high probabil-
ity).
Let A be an n n matrix. Then
Ax = 0
has solutions x 6= 0 (x 2 Rn
) i¤ A is not full rank.
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