Page 81 - Statistics and Data Analysis in Geology

Matrix Algebra

such as S-PLUS@ , will provide all of the mathematical computation power you are
likely to need for applications in the Earth sciences. We have attempted to present,
in as painless a manner as possible, the rudiments of beginning matrix algebra. As
stated at the conclusion of Chapter 2, statistics is too large a subject to be covered
in one chapter, or even one book. Matrix algebra also is an impossibly large subject
to encompass in these few pages. However, you should now have some insight
into matrix methods that will enable you to understand the computational basis of
techniques we will cover in the remainder of this book.

EXERCISES

Exercise 3.1
File BHTEMP.TXT contains 15 bottomhole temperatures (BHT’s) measured in the
Mississippian interval in wells in eastern Kansas. The measurements are in degrees
Fahrenheit. Convert the vector of temperatures to degrees Celsius using matrix
algebra.

Exercise 3.2

The following two matrices are defined:
0 ‘1 B=[-3 -2 -4 ‘1

A=[ -2

Compute the matrix products, AB and B A. Two matrices which exhibit the property
that will be apparent are said to be commutative. Demonstrate that for commuta-
tive matrices, A-~B-~ = (ABP
Consider the following two matrices,
c= [o 4 0 0 2] .=[: : i]
2 1 0
1 -1
3

Compare the determinant, (CDI, of the matrix product to the product, (CI - IDI,
of the determinants of the two matrices. The result you obtain is general. Deter-
mine if ICI + ID( = IC + DI. This result also is general. For the matrices C and D,
demonstrate that (CD)T = DTCT. Using matrix C, show that (C-l)T = (CT)-l.

Exercise 3.3

File MAGNET1T.m contains the proportions of olivine, magnetite, and anorthite
estimated by point-counting thin sections from 15 hand specimens collected at a
magnetite deposit in the Laramie Range of Wyoming. The specific gravity is 3.34 for
olivine, 2.76 for anorthite, and 5.20 for magnetite. Using matrix algebra, estimate
the specific gravity of the 15 samples.

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