Linear Algebra

Linear Algebra is the branch of mathematics aimed at solving systems of linear equations with a ﬁnite number of unknowns.

Linear Algebra Mathematics

Tác giả: Isaiah Lankham, Bruno Nachtergaele, & Anne Schilling
Nhà xuất bản: University of California, Davis
Nguồn: LibreTexts
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

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Mục lục· 77 mục

01: What is linear algebra
1.E: Exercises for Chapter 1
02: Introduction to Complex Numbers
2.01: Deﬁnition of Complex Numbers
2.02: Operations on complex numbers
2.03: Polar Form and Geometric Interpretation
2.E: Exercises for Chapter 2
03: 3. The fundamental theorem of algebra and factoring polynomials
3.01: The Fundamental Theorem of Algebra
3.02: Factoring polynomials
3.E: Exercises for Chapter 3
04: Vector spaces
4.01: Deﬁnition of vector spaces
4.02: Elementary properties of vector spaces
4.03: Subspaces
4.04: Sums and direct sum
4.E: Exercises for Chapter 4
05: Span and Bases
5.01: Linear Span
5.02: Linear Independence
5.03: Bases
5.04: Dimension
5.E: Exercises for Chapter 5
06: Linear Maps
6.01: Denition and elementary properties
6.02: Null spaces
6.03: Ranges
6.04: Homomorphisms
6.05: The dimension formula
6.06: The matrix of a linear map
6.07: Invertibility
6.E: Exercises for Chapter 6
07: Eigenvalues and Eigenvectors
7.01: Invariant Subspaces
7.02: Eigenvalues
7.03: Diagonal matrices
7.04: Existence of Eigenvalues
7.05: Upper Triangular Matrices
7.06: Diagonalization of (2times 2) matrices and Applications
7.E: Exercises for Chapter 7
08: Permutations and the Determinant
8.01: Permutations
8.02: Determinants
8.E: Exercises for Chapter 8
09: Inner product spaces
9.01: Inner Products
9.02: Norms
9.03: Orthogonality
9.04: Orthonormal bases
9.05: The Gram-Schmidt Orthogonalization procedure
9.06: Orthogonal projections and minimization problems
9.E: Exercises for Chapter 9
10: Change of bases
10.01: Coordinate Vectors
10.02: 10.2 Change of basis transformation
10.E: Exercises for Chapter 10
11: The Spectral Theorem for normal linear maps
11.01: Self-adjoint or hermitian operators
11.02: Normal operators
11.03: Normal operators and the spectral decomposition
11.04: Diagonalization
11.05: Positive operators
11.06: Polar decomposition
11.07: Singular-value decomposition
11.E: Exercises for Chapter 11
12: Supplementary notes on matrices and linear systems
12.01: From linear systems to matrix equations
12.02: Matrix arithmetic
12.03: Solving linear systems by factoring the coefficient matrix
12.04: Matrices and linear maps
12.05: Special operations on matrices
12.E: Exercises
13: Appendices
13.01: The Language of Sets and Functions
13.02: Summary of Algebraic Structures
13.03: Some Common Mathematical Symbols and Abbreviations
13.04: Summary of Notation Used