Matrix by a constant

The development of vector and parallel computers has greatly influenced methods for solving linear systems, for such computers greatly speed up many matrix and vector computations. For instance, the addition of two n-dimensional vectors or of two nxn matrices or multiplication of such a vector or of such a matrix by a constant requires n or arithmetic operations, but all of them can be performed in one parallel step if n or processors are available. Such additional power dramatically increased the previous ability to solve large linear systems in a reasonable amount of time. This development also required revision of the previous classification of known algorithms in order to choose algorithms most suitable for new computers. For instance, Jordan s version of Gaussian elimina-... 

A diagonal matrix is one with zeros everywhere except on the principal diagonal (running from upper left to lower right corner) that is Atj = 0 unless i = j. The unit matrix E is a special diagonal matrix whose diagonal elements are each unity. Therefore E = 5,y ]. The unit matrix has the property that EA = AE = A. A constant matrix, C, is a multiple of the unit matrix by a constant that is C = cE. 

There is an algebra for matrices. We can multiply a matrix by a constant ... 

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