Practice Makes Perfect Linear Algebra 9780071778442, 0071778446, 9780071778435, 0071778438
Expert instruction and plenty of practice to reinforce advanced math skills Presents concepts with application to natur
253 109 25MB
English Year 2013
Table of contents :
Preface
1 Systems of linear equations and matrices
Systems of linear equations
General systems of linear equations
Matrices
Row transformations and equivalence of matrices
Row-echelon form
Homogeneous systems
2 Matrix algebra
Matrix arithmetic
Inverse of a square matrix
Properties of invertible matrices
Matrix solutions of systems of linear equations
Transpose of a matrix
3 Graphing calculators and matrices
Matrix menu
Inputting and editing a matrix
Matrix arithmetic
Calculating determinants
Transpose of a matrix
Solving linear systems using Gauss-Jordan elimination
Solving linear systems using X = A–1C
4 Special types of square matrices
Nonsingular matrices
Triangular, diagonal, and scalar matrices
Involutory, idempotent, and nilpotent matrices
Symmetric and skew-symmetric matrices
Orthogonal matrices
Hermitian and skew-Hermitian matrices
5 Determinants
Determinant of a square matrix
Cramer’s rule
Properties of determinant
6 Vectors in Rn
Vectors in two dimensions
Dot product of vectors
Vectors in Rn
Vectors as matrices
7 Vector spaces
Definitions and terminology of vector spaces
Linear independence
Basis
Dimension
Row space, column space, and null space
Rank and nullity
8 Inner product spaces
Definition and terminology for inner product spaces
Norm of a vector in an inner product space
Cauchy-Schwarz inequality and properties of the norm
Orthogonality in inner product spaces
Gram-Schmidt procedure
9 Linear transformations
Definition and terminology for linear transformations
Kernel and image of a linear transformation
Matrix representations of linear transformations
Change of basis
Algebra of linear transformations
Linear operators on R 2 and R 3
10 Eigenvalues and eigenvectors
The eigenvalue problem
Useful properties of eigenvalues
Diagonalization
Answer key
Preface
1 Systems of linear equations and matrices
Systems of linear equations
General systems of linear equations
Matrices
Row transformations and equivalence of matrices
Row-echelon form
Homogeneous systems
2 Matrix algebra
Matrix arithmetic
Inverse of a square matrix
Properties of invertible matrices
Matrix solutions of systems of linear equations
Transpose of a matrix
3 Graphing calculators and matrices
Matrix menu
Inputting and editing a matrix
Matrix arithmetic
Calculating determinants
Transpose of a matrix
Solving linear systems using Gauss-Jordan elimination
Solving linear systems using X = A–1C
4 Special types of square matrices
Nonsingular matrices
Triangular, diagonal, and scalar matrices
Involutory, idempotent, and nilpotent matrices
Symmetric and skew-symmetric matrices
Orthogonal matrices
Hermitian and skew-Hermitian matrices
5 Determinants
Determinant of a square matrix
Cramer’s rule
Properties of determinant
6 Vectors in Rn
Vectors in two dimensions
Dot product of vectors
Vectors in Rn
Vectors as matrices
7 Vector spaces
Definitions and terminology of vector spaces
Linear independence
Basis
Dimension
Row space, column space, and null space
Rank and nullity
8 Inner product spaces
Definition and terminology for inner product spaces
Norm of a vector in an inner product space
Cauchy-Schwarz inequality and properties of the norm
Orthogonality in inner product spaces
Gram-Schmidt procedure
9 Linear transformations
Definition and terminology for linear transformations
Kernel and image of a linear transformation
Matrix representations of linear transformations
Change of basis
Algebra of linear transformations
Linear operators on R 2 and R 3
10 Eigenvalues and eigenvectors
The eigenvalue problem
Useful properties of eigenvalues
Diagonalization
Answer key
- Author / Uploaded
- Sandra Luna McCune
- William D. Clark
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