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Answers to Exercises

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 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 alpha beta gamma

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