Expert instruction and plenty of practice to reinforce advanced math skills Presents concepts with application to natur
456 130 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