MATH 253 Notes

All files are in PDF format.

• Why study Linear Algebra?
• Systems of equations
• Properties of matrices
• Row operations
• Reduced Row Echelon Form
• Homogeneous systems of equations and stochastic matrices
• Review for Exam 1
• Vector spaces
• Vector spaces and subspaces
• Linear combinations and span
• Linear independence
• Linear independence continued
• Basis and dimension
• Basis and dimension continued
• The rank of a matrix
• Rank, nullity, and the Rank-Nullity Theorem
• Review for Exam 2
• Linear transformations
• Properties of linear transformations
• The matrix of a linear transformation
• Change of basis
• Column operations
• Determinants
• Properties of determinants
• Cramer's Rule
• Review for exam 3
• Inner product spaces and Gram-Schmidt
• Eigenstuff
• Diagonalization
• Diagonalization (continued)
• Page Rank and Schur's Theorem
• The Cayley-Hamilton Theorem
• Jordan Canonical Form
• Review for final

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Last updated 9/19/2022.