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Math 2331 { Linear Algebra
www.math.uh.eduJiwen He, University of Houston Math 2331, Linear Algebra 8 / 14. 4.5 The Dimension of a Vector Space DimensionBasis Theorem Dimensions of Subspaces: Theorem Theorem (11) Let H be a subspace of a nite-dimensional vector space V. Any linearly independent set in H can be expanded, if necessary, to a
Math 2331 { Linear Algebra
www.math.uh.edu5.3 Diagonalization DiagonalizationTheoremExamples Diagonalization: Example Example Diagonalize the following matrix, if possible. A = 2 4 2 4 6 0 2 2 0 0 4 3 5: Since this matrix is triangular, the eigenvalues are 1 = 2 and 2 = 4. By solving (A I)x = 0 for each eigenvalue, we would nd the following: 1 = 2 : v 1 = 2 4 1 0 0 3 5, 2 = 4 : v 2 = 2 ...