Handbook of Methods in Cultural Anthropology by H. Russell Bernard, Clarence C. Gravlee

By H. Russell Bernard, Clarence C. Gravlee

This guide of anthropology tools defines and describes anthropological fieldwork in perform. The authors study historic equipment, surveys, linguistic equipment, comparative study, social intervention, and visible anthropology.

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28: Let ⎡1 ⎢2 ⎢ ⎢0 ⎢ X = ⎢1 ⎢5 ⎢ ⎢1 ⎢2 ⎣ ⎡1 ⎢1 ⎢ ⎢1 Xt X = ⎢ ⎢1 ⎢0 ⎢ ⎣⎢1 2 1 2 2 1 2 0 1 1 3 1 1 ⎡1 ⎢1 ⎢ ⎢1 = ⎢ ⎢1 ⎢0 ⎢ ⎢⎣1 ⎡0 ⎢1 ⎢ ⎢1 + ⎢ ⎢3 ⎢1 ⎢ ⎢⎣1 1 0 1 1 3 2 5 1 0 2 1 3 1⎤ 1 ⎥⎥ ⎡0 0 ⎥ ⎢1 ⎥⎢ 1 ⎥ ⎢5 2 ⎥ ⎢⎣1 ⎥ 4 ⎥⎦ 1 0 1 1 3 2 1 1 1 0 1 1 1 5 1 0 2 1 3 1 2 1 1 0 0 1 1 1 0 1 2 4 1 2 3 1 2 1 5 0 1 1 3 1 2 0 1⎤ 2 ⎥⎥ 1⎥ ⎥ 2⎥ . 3⎥ ⎥ 4⎥ 2 ⎥⎦ 2⎤ 1 ⎥⎥ 1⎥ ⎥ 5⎥ 0⎥ ⎥ 2 ⎦⎥ ⎡1 ⎢2 ⎢ ⎢0 ⎢ ⎢1 ⎢5 ⎢ ⎢1 ⎢2 ⎣ 1 1 1 0 1 1 1 1 2 1 1 0 0 1 1 2 3 1 2 1 5 0 1 1 3 1 2 0 1⎤ 2 ⎥⎥ 1⎥ ⎥ 2⎥ 3⎥ ⎥ 4⎥ 2 ⎥⎦ 2⎤ 1 ⎥⎥ 2 ⎥ ⎡1 1 1 1 0 1 ⎤ ⎥ 2 ⎥ ⎢⎣ 2 1 2 2 1 2 ⎥⎦ 1⎥ ⎥ 2 ⎥⎦ 1 0 1 1 1 1 0 0 3 1 2 1 49 ⎡2⎤ ⎢ ⎥ 1 1 ⎤ ⎢1 ⎥ 3 2 ⎥⎥ ⎢ 1 ⎥ + ⎢ ⎥ [2 1 1 | 5 0 | 2] 1 3⎥ ⎢5 ⎥ ⎥ 2 4⎦ ⎢0 ⎥ ⎢ ⎥ ⎢⎣ 2 ⎥⎦ ⎡ ⎡1 ⎢⎢ ⎢ ⎢1 ⎢ ⎢⎣1 ⎢ ⎢ ⎡1 = ⎢⎢ ⎢ ⎣0 ⎢ ⎢ [1 ⎢⎣ ⎡ ⎢ ⎡0 ⎢⎢ ⎢ ⎢1 ⎢ ⎢⎣1 ⎢ ⎢ ⎢ ⎢ ⎡3 ⎢⎢ ⎢ ⎣1 ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ [1 ⎢ ⎢⎣ 2⎤ ⎡1 1 1 ⎤ 1 ⎥⎥ ⎢ 2 1 2 ⎥⎦ 2 ⎥⎦ ⎣ 2⎤ ⎡1 1 1 ⎥⎦ ⎢⎣ 2 1 ⎡1 1 2] ⎢ ⎣2 1 ⎡0 1 5 1⎤ ⎢ 1 0 1 1 ⎥⎥ ⎢ ⎢5 1 0 0 ⎥⎦ ⎢ ⎣1 ⎡0 1 2 1 ⎤ ⎢⎢1 3 1 2 ⎥⎦ ⎢ 5 ⎢ ⎣1 1 0 1 1 ⎡0 ⎢1 2 3 4] ⎢ ⎢5 ⎢ ⎣1 1 0 1 1 1 0 1 1 1⎤ 1 ⎥⎥ 0⎥ ⎥ 0⎦ 1⎤ 1 ⎥⎥ 0⎥ ⎥ 0⎦ 1⎤ 1 ⎥⎥ 0⎥ ⎥ 0⎦ ⎡1 2 ⎤ ⎢1 1 ⎥ ⎡1 ⎢ ⎥ ⎢2 ⎢⎣1 2 ⎥⎦ ⎣ 1 ⎤ ⎡1 2⎤ ⎡ 1 2 ⎥⎦ ⎢⎣0 1 ⎥⎦ ⎢⎣ 2 1⎤ ⎡1 [1 2] ⎢ ⎥ 2⎦ ⎣2 ⎡3 ⎡0 1 5 1⎤ ⎢ ⎢1 0 1 1 ⎥ ⎢1 ⎢ ⎥ ⎢2 ⎢⎣1 1 0 0 ⎥⎦ ⎢ ⎣1 ⎡3 ⎢ ⎡3 1 2 1 ⎤ ⎢ 1 ⎢1 3 1 2 ⎥ ⎢ 2 ⎣ ⎦ ⎢ ⎣1 ⎡3 ⎢1 [1 2 3 4] ⎢⎢ 2 ⎢ ⎣1 ⎡ ⎡2⎤ ⎢⎢ ⎥ ⎢ ⎢1 ⎥ [ 2 1 1] ⎢ ⎢⎣1 ⎥⎦ + ⎢ ⎢ ⎡5⎤ ⎢ ⎢ 0 ⎥ [ 2 1 1] ⎢⎣ ⎦ ⎢ [ 2][ 2 1 1] ⎣ ⎡ 2⎤ ⎢1 ⎥ 5 0 ] ⎢ ⎥[ ⎢⎣1 ⎥⎦ ⎡5⎤ ⎢ 0 ⎥ [5 0] ⎣ ⎦ [ 2][5 50 0] ⎤ ⎡1 2 ⎤ ⎢1 1 ⎥ ⎡ 1 ⎤ ⎥ ⎢ ⎥ ⎢ 2⎥ ⎥ ⎢⎣1 2 ⎥⎦ ⎣ ⎦ ⎥ ⎥ 0⎤ ⎡1 2⎤ ⎡1 ⎤ ⎥ + 1 ⎥⎦ ⎢⎣ 0 1 ⎥⎦ ⎢⎣ 2⎥⎦ ⎥⎥ 0⎤ ⎡1 ⎤ ⎥ [1 2] ⎢ ⎥ ⎥ ⎥ 1⎦ ⎣ 2 ⎦ ⎥⎦ 0⎤ 1 ⎥⎦ 1⎤ 3 ⎥⎥ 1⎥ ⎥ 2⎦ 1⎤ 3 ⎥⎥ 1⎥ ⎥ 2⎦ 1⎤ 3 ⎥⎥ 1⎥ ⎥ 2⎦ ⎡1 ⎤ ⎤ ⎡0 1 5 1⎤ ⎢ ⎥ ⎥ ⎢1 0 1 1 ⎥ ⎢ 2⎥ ⎥ ⎢ ⎥ ⎢ 3⎥ ⎥ ⎢⎣1 1 0 0 ⎥⎦ ⎢ ⎥ ⎥ ⎣ 4⎦ ⎥ ⎥ ⎡1 ⎤ ⎥ ⎢ ⎥ ⎡3 1 2 1 ⎤ ⎢ 2 ⎥ ⎥ ⎢1 3 1 2 ⎥ ⎢ 3 ⎥ ⎥ ⎥ ⎣ ⎦ ⎢ ⎥⎥ ⎣4⎦ ⎥ ⎡1 ⎤ ⎥ ⎢2⎥ ⎥ [1 2 3 4] ⎢⎢ 3⎥⎥ ⎥⎥ ⎢ ⎥⎥ ⎣ 4 ⎦ ⎥⎦ ⎡2⎤ ⎤ ⎢1 ⎥ 2 ⎥ ⎢ ⎥[ ]⎥ ⎢⎣1 ⎥⎦ ⎥ ⎥ = ⎡5⎤ ⎥ ⎢ 0 ⎥ [ 2 ]⎥ ⎣ ⎦ ⎥ [ 2][ 2] ⎥⎦ ⎡5 ⎢3 ⎢ ⎢5 ⎢ ⎢5 ⎢2 ⎢ ⎣⎢ 5 3 2 3 3 1 3 5 3 5 5 2 5 5 3 5 5 2 5 2 1 2 2 1 2 ⎡4 ⎢2 ⎢ ⎢2 ⎢ ⎢10 ⎢0 ⎢ ⎢⎣ 4 = 5 ⎤ ⎡ 27 6 3 ⎥⎥ ⎢⎢ 6 3 5⎥ ⎢ 1 1 ⎥ + ⎢ 5 ⎥ ⎢12 6 2 ⎥ ⎢10 4 ⎥ ⎢ 5 ⎦⎥ ⎣⎢ 21 8 2 1 1 5 0 2 1 1 2 4 4 3 12 6 4 15 10 15 10 4 4 10 15 18 21⎤ 8 ⎥⎥ 3⎥ ⎥ + 15 ⎥ 18 ⎥ ⎥ 30 ⎦⎥ 2 10 0 4 ⎤ 1 5 0 2 ⎥⎥ 1 5 0 2⎥ ⎥ 5 25 0 10 ⎥ 0 0 0 0⎥ ⎥ 2 10 0 4 ⎥⎦ ⎡ 36 11 8 27 12 ⎢ 11 6 5 14 5 ⎢ ⎢ 8 5 8 14 6 ⎢ ⎢ 27 14 14 45 12 ⎢12 5 6 12 16 ⎢ ⎢⎣ 30 13 10 30 20 30 ⎤ 13 ⎥⎥ 10 ⎥ ⎥.

31⎥ ⎢ 0 ⎥ ⎣ ⎦ is a 9 × 1 column fuzzy matrix.

1 0 5 ⎥ −2 0 10 ⎥ ⎥ 0 0 0 ⎥⎦ We leave it for the reader to verify that (Va V'b)' = Vb V'a. 19: We just recall if ⎡3⎤ v = ⎢⎢ 4 ⎥⎥ ⎢⎣ 7 ⎥⎦ is a column vector and v' the transpose of v is a row vector then we have ⎡3⎤ v'v = [3 4 7 ] ⎢⎢ 4 ⎥⎥ ⎣⎢7 ⎦⎥ = 32 + 42 + 72 = 74. Thus if V'x = [x1 x2 … xn] 31 ⎡ x1 ⎤ ⎢x ⎥ V'x Vx = [x1 x2 … xn] ⎢ 2 ⎥ ⎢ ⎥ ⎢ ⎥ ⎣xn ⎦ = x12 + x 22 + … + x n2 . , 1'vx = v'x1 = ∑x i where ⎡ x1 ⎤ ⎢x ⎥ vx = ⎢ 2 ⎥ ⎢ ⎥ ⎢ ⎥ ⎣xn ⎦ and ∑ x i = x1 + x2 + … + xn. We have the following types of products defined.

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