ABSTRACT
A generalization of a vector, that is, an ordered array of numbers, determines the magnitude and direction of the vector. A further generalization is that of an n × m matrix A = { a i j } = ( a i j ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315215136/85154af4-39d8-4b43-ae90-9b7d84af8606/content/eq78.tif"/> , which is shown below: () A = [ a 11 a 12 ⋯ a 1 m a 21 a 22 ⋯ a 2 m ⋮ ⋮ ⋮ a n 1 a n 2 ⋯ a n m ] https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315215136/85154af4-39d8-4b43-ae90-9b7d84af8606/content/eq79.tif"/> with a typical element a ij , where i = 1 , 2 , … , n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315215136/85154af4-39d8-4b43-ae90-9b7d84af8606/content/eq80.tif"/> and j = 1 , 2 , … , m https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315215136/85154af4-39d8-4b43-ae90-9b7d84af8606/content/eq81.tif"/> .
