In a p dimension space
A Á B ¼
p
X
i¼1
A i B i
Properties of Matrices
A matrix is an array of numbers or symbols with the following general form
a 11 a 12 a 13
a 21 a 22 a 23
a 31 a 32 a 33
2
4
3
5
The square brackets indicate the matrix, as opposite to a determinant. It can be used
[a ij ] as a symbol, meaning that the matrix has i rows and j columns. a ij is an element of
the ith row and jth column. If the number of rows and columns is equal, the matrix is
called square. In a square matrix, the elements a ij , where i = j, are called diagonal
elements, the others are called off-diagonal elements. If these later are 0, the matrix is
called diagonal. If the diagonal elements are 1, the matrix is called unit matrix
Fig. A.1 Vector A and B separated by an angle h and placed in an xy space
Appendix
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