By Magar E. Mager
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Extra resources for Data Analysis in Biochemistry and Biophysics
3 - 1 . 7) the only sets we will generally be concerned with are sets of real n u m b e r s . (2D (2D AUB ARB (2D Δ\ Β A c C Fig. 3-1. Venn diagrams. In the diagram labeled A the universal set is the rectanc gle in which A and Β are enclosed and the shaded area is A .
S p e c i a l M a t r i c e s W h e n dealing with matrices we frequently encounter some special matrices. g. 0 0 0 (2-11) 0 0 0 24 2 Matrices or 0 0 0 0 0 0 0 0 0 (2-12) A square matrix has the same n u m b e r or rows and columns. Matrices (2-3) and (2-12) are square matrices. A diagonal matrix is a square matrix whose only nonzero elements are on the main diagonal. M a t r i x (2-13) depicted below is a diagonal matrix. 0 0 0 «44. (2-13) If in a k where k is some «22 .. = «11 = constant, t h e n the diagonal matrix is called a scalar matrix.
2-13) If in a k where k is some «22 .. = «11 = constant, t h e n the diagonal matrix is called a scalar matrix. 1 01 1. (2-14) 0 1 0 (2-15) SQUARE M A T R I C E S If A and Β are square matrices such that AB = ΒΑ (2-16) then A and Β are said to c o m m u t e . e. A I n — I nA (2-17) in addition each matrix commutes with itself A A = AA. N o w if we 2 3 2 4 3 n n _ 1 define A = AA, A = A A , A = A A , . . , A = A A , it is easy to n m w n n+m show, by induction, that A A = A A = A . If for a matrix A we +1 have A * = A, where k is a positive integer, t h e n A is said to be nil2 potent with index k.
Data Analysis in Biochemistry and Biophysics by Magar E. Mager