LINEAR ALGEBRA

By KENNETH LEWIS

CONTENTS NOTATION AND TERMINOLOGY FIELDS VECTOR SPACES OVER A ?ELD ALGEBRAS OVER A ?ELD LINEAR INDEPENDENCE AND DIMENSION LINEAR TRANSFORMATIONS THE ENDOMORPHISM ALGEBRA OF A VECTOR SPACE REPRESENTATION OF LINEAR TRANSFORMATIONS BY MATRICES THE ALGEBRA OF SQUARE MATRICES 10 SYSTEMS OF LINEAR EQUATIONS 11 DETERMINANTS 12 EIGENVALUES AND EIGENVECTORS 13 KRYLOV SUBSPACES 14 THE DUAL SPACE 15 INNER PRODUCT SPACES 16 ORTHOGONALITY 17 SELFADJOINT ENDOMORPHISMS 18 UNITARY AND NORMAL ENDOMORPHISMS 19 MOORE-PENROSE PSEUDOINVERSES 20 BILINEAR TRANSFORMATIONS AND FORMS