Algebra lineal

Páginas: 226 (56265 palabras) Publicado: 10 de marzo de 2010
Linear Algebra
Jim Hefferon

1 3

2 1

1 3

2 1
x1 · 1 3

2 1

x1 · 1 2 x1 · 3 1
6 8

2 1

6 2 8 1

Notation R N C {. . . . . .} ... V, W, U v, w 0, 0V B, D En = e1 , . . . , en β, δ RepB (v) Pn Mn×m [S] M ⊕N V ∼W = h, g H, G t, s T, S RepB,D (h) hi,j |T | R(h), N (h) R∞ (h), N∞ (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×m matrices span of the set S direct sum of subspaces isomorphic spaces homomorphisms, linear maps matrices transformations; maps from a space to itself square matrices matrix representing the map hmatrix 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 alpha beta gamma delta epsilon zeta eta theta character α β γ δ ζ η θ name iota kappa lambda mu nu xi omicron pi character ι κ λ µ ν ξ o π name rho sigma tau upsilon phi chi psi omega character ρ σ τ υ φ χ ψ ω

Cover. This isCramer’s Rule for the system x1 + 2x2 = 6, 3x1 + x2 = 8. The size of the ﬁrst box is the determinant shown (the absolute value of the size is the area). The size of the second box is x1 times that, and equals the size of the ﬁnal box. Hence, x1 is the ﬁnal determinant divided by the ﬁrst determinant.

Preface

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