Matrices and Transformations
This text stresses the use of matrices in study of transformations of the plane. Familiarizes reader with role of matrices in abstract algebraic systems and illustrates its effective use as mathematical tool in geometry. Includes proofs of most theorems. Answers to odd-numbered exercises.
What people are saying - Write a review
We haven't found any reviews in the usual places.
Other editions - View all
angle augmented matrix called characteristic equation complex numbers conic Consider corresponding elements diagonal elements diagonal matrix eigenvalues eigenvector associated elementary row transformation elements of row equal Example 1 Determine Exercises 1n Exercises exists Hamilton-Cayley Theorem Hence Hermitian matrix homogeneous coordinates image points image with respect invariant vector spaces linear equations linear homogeneous transformation linearly independent magnification maps each point matrix equation matrix of coefficients matrix of order matrix representing multiplicative inverse multiply the elements nonsingular matrix nonzero scalar one-to-one mapping order three orthogonal matrix plane represented plane that maps plane with respect Proof proper orthogonal matrix Prove quadratic form rank real numbers real symmetric matrix reflection matrix representing a rotation rotation matrix row transformation matrices scalar multiple set of eigenvectors set of points shear parallel similar matrices single-valued mapping skew-Hermitian matrix skew-symmetric matrix square matrix system of linear Theorem 1-5 transformation represented transpose unit eigenvectors x-axis