Page 151 - Numerical Analysis Using MATLAB and Excel

Summary

• A scalar matrix is a square matrix where a 11 = a 22 = a 33 = … = a nn = k and is a scalar.
k
A scalar matrix with k = 1 , is called an identity matrix . I

•The MATLAB eye(n) function displays an n × n identity matrix and the eye(size(A)) func-
tion displays an identity matrix whose size is the same as matrix .
A
A
• The transpose of a matrix , denoted as A T , is the matrix that is obtained when the rows and
columns of matrix are interchanged.
A
• The determinant of a square matrix where
A

a 11 a 12 a 13 … a 1n
a 21 a 22 a 23 … a 2n
A = a 31 a 32 a 33 … a 3n
……… … …

a n1 a n2 a n3 … a nn

is denoted as detA and it is defined as

detA = a a a …a nn + a a a …a n1 + a a a …a n2 + …
13 24 35
12 23 34
11 22 33
a …a a … a–– …a a – a …a a – …
n1 22 13 n2 23 14 n3 24 15
• If from a matrix be defined as
A
a 11 a 12 a 13 … a 1n
a 21 a 22 a 23 … a 2n
A = a 31 a 32 a 33 … a 3n
……… … …

a n1 a n2 a n3 … a nn

we remove the elements of its ith row, and jth column, the determinant of the remaining

n – 1 square matrix is called the minor of determinant , and it is denoted as M .
A
ij
• The signed minor –( 1 ) i + j M ij is called the cofactor of a ij and it is denoted as α ij .

• Let be a square matrix of any size; the value of the determinant of is the sum of the prod-
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ucts obtained by multiplying each element of any row or any column by its cofactor. We must
use this procedure to find the determinant of a matrix of order 4 or higher.
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Numerical Analysis Using MATLAB® and Excel®, Third Edition 4−33
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