tailieunhanh - Sách: Linear Algebra

complex numbers set of . . . such that . . . sequence; like a set but order matters vector spaces vectors zero vector, zero vector of V bases standard basis for Rn basis vectors matrix representing the vector set of n-th degree polynomials set of n×m matrices span of the set S direct sum of subspaces isomorphic spaces homomorphisms matrices transformations; maps from a space to itself square matrices matrix representing the map h matrix entry from row i, column j determinant of the matrix T rangespace and nullspace of the map h generalized rangespace and nullspace Lower case Greek. | _ fteĩ0Đ Notation R N C . I . ị V W U V w 0 V B D En e1 . en RepB V Pn Mn m íặ M N V W h g H G t s T S ReP B D h h ij T R h N h R1 h N1 h real numbers natural numbers 0 1 2 . complex numbers set of . such that . sequence like a set but order matters vector spaces vectors zero vector zero vector of V bases standard basis for Rn basis vectors matrix representing the vector set of n-th degree polynomials set of n xm matrices span of the set S direct sum of subspaces isomorphic spaces homomorphisms matrices transformations maps from a space to itself square matrices matrix representing the map h matrix entry from row i column j determinant of the matrix T rangespace and nullspace of the map h generalized rangespace and nullspace Lower case Greek alphabet name symbol name symbol name symbol alpha a iota b rho p beta p kappa K sigma Ơ gamma lambda X tau T delta 5 mu g upsilon V epsilon nu phi Á zeta c xi chi  eta g omicron 0 psi à theta e pi 7Ĩ omega Jj Cover. This is Cramer s Rule applied to the system x 2y 6 3x y 8. The area of the first box is the determinant shown. The area of the second box is x times that and equals the area of the final box. Hence x is the final determinant divided by the first determinant. Preface In most mathematics programs linear algebra is taken in the first or second year following or along with at least one course in calculus. While the location of this course is stable lately the content has been under discussion. Some instructors have experimented with varying the traditional topics trying courses focused on applications or on the computer. Despite this entirely healthy debate most instructors are still convinced I think that the right core material is vector spaces linear maps determinants and eigenvalues and eigenvectors. Applications and computations certainly can have a part to play but most mathematicians agree that the themes of the course should remain unchanged. Not that all is fine with the traditional course. Most of us do .