note - MATH1104 Notes By Eric Hua Contents Chapter 1....

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH1104 Notes By Eric Hua Contents Chapter 1. Linear Equations in Linear Algebra 3 1.1 Systems of Linear Equations . . . . . . . . . . . . . . . 3 1.2 Row reduction and echelon forms . . . . . . . . . . . 5 1.3 Vector Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 Equation A~x = ~ b . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5 Solution sets of linear systems . . . . . . . . . . . . . . 11 1.6 Applications of Linear Systems . . . . . . . . . . . . . 13 1.7 Linear Independence . . . . . . . . . . . . . . . . . . . . . . . 15 1.8 Introduction to Linear Transformation . . . . . . . 15 1.9 The matrix of a linear transformation . . . . . . . . 16 1.10 Linear Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Chapter 2. Matrix Algebra 20 2.1 Matrix operations . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2 The Inverse of a Matrix . . . . . . . . . . . . . . . . . . . . 22 2.3 Characterization of Invertible Matrices . . . . . . 23 2.8 Subspaces of R n . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.9 Dimension and Rank . . . . . . . . . . . . . . . . . . . . . . . 26 Chapter 3. Determinants 28 3.1 Introduction to Determinants . . . . . . . . . . . . . . . 28 3.2 Properties of Determinants . . . . . . . . . . . . . . . . . 29 3.3 Cramers rule, volume and linear transforma- tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Chapter 5. Eigenvalues and Eigenvectors 33 5.1 Eigenvectors and Eigenvalues . . . . . . . . . . . . . . . 33 5.2 The Characteristic Equation . . . . . . . . . . . . . . . . 34 5.3 Diagonalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1 Appendix B: Complex Numbers . . . . . . . . . . . . . . . . 37 5.5 Complex Eigenvalues . . . . . . . . . . . . . . . . . . . . . . . 39 Chapter 6. Orthogonality and Least Squares 41 6.1 Inner Product, Length and Orthogonality . . . . 41 6.2 Orthogonal Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 6.3 Orthogonal Projections . . . . . . . . . . . . . . . . . . . . . 46 2 Chapter 1. Linear Equations in Linear Algebra 1.1 Systems of Linear Equations Definition 1 A linear equation in variables x 1 ,x 2 ,...,x n has the form a 1 x 1 + a 2 x 2 + a 3 x 3 + + a n x n = d where the numbers a 1 ,...,a n R are the equations coefficients and d R is the constant. An n-tuple ( s 1 ,s 2 ,...,s n ) R n is a solution of, or satisfies, that equation if substituting the numbers s 1 , ..., s n for the variables gives a true statement: a 1 s 1 + a 2 s 2 + ... + a n s n = d . A system of linear equations a 1 , 1 x 1 + a 1 , 2 x 2 + + a 1 ,n x n = d 1 a 2 , 1 x 1 + a 2 , 2 x 2 + + a 2 ,n x n = d 2 ....
View Full Document

Page1 / 48

note - MATH1104 Notes By Eric Hua Contents Chapter 1....

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online