- 8.9.1: In 1 and 2, verify that the given matrix satisfies its own characte...
- 8.9.2: In 1 and 2, verify that the given matrix satisfies its own characte...
- 8.9.3: In 3-10, use the method of this section to compute Am. Use this res...
- 8.9.4: In 3-10, use the method of this section to compute Am. Use this res...
- 8.9.5: In 3-10, use the method of this section to compute Am. Use this res...
- 8.9.6: In 3-10, use the method of this section to compute Am. Use this res...
- 8.9.7: In 3-10, use the method of this section to compute Am. Use this res...
- 8.9.8: In 3-10, use the method of this section to compute Am. Use this res...
- 8.9.9: In 3-10, use the method of this section to compute Am. Use this res...
- 8.9.10: In 3-10, use the method of this section to compute Am. Use this res...
- 8.9.11: In 11 and 12, show that the given matrix has an eigenvalue A1 of mu...
- 8.9.12: In 11 and 12, show that the given matrix has an eigenvalue A1 of mu...
- 8.9.13: Show that A = 0 is an eigenvalue of each matrix. In this case, the ...
- 8.9.14: In his workliber Abbaci, published in 1202, Leonardo Fibonacci of P...
- 8.9.15: In 15 and 16, use the procedure illustrated in (9) to find A -1 .A=...
- 8.9.16: In 15 and 16, use the procedure illustrated in (9) to find A -1 .A=...
- 8.9.17: A nonzero n X n matrix A is said to be nilpotent of index m if mis ...
- 8.9.18: (a) Explain why any nilpotent matrix A is singular. [Hint: A 2 - A1...
Solutions for Chapter 8.9: Powers of Matrices
Full solutions for Advanced Engineering Mathematics | 5th Edition
Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.
Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.
Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
Chi-square (or chi-squared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.
Coeficient of determination
See R 2 .
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .
Another name for factors that are arranged in a factorial experiment.
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.
Error mean square
The error sum of squares divided by its number of degrees of freedom.
Fisher’s least signiicant difference (LSD) method
A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.
Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .