Matrix Algebra Operations

May 29th, 2015
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In this chapter, we will discuss the elementary operations of addition, subtraction, multiplication, and inversion, a matrix algebra analogue of division of scalar numbers. Subsequently, we will turn our attention to powers of matrices and to

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Matrix Algebra OperationsIn this chapter, we will discuss the elementary operations of addition, subtraction, multiplication, and inversion, a matrix algebra analogue of division of scalar numbers. Subsequently, we will turn our attention to powers of matrices and to operations involving scalar numbers and matrices, scalar numbers and vectors, and vectors and matrices.The operations on matrices differ from similar operations of scalar algebra in several respects. The matrix algebra operations, in general, are not commutative and attention must be paid to whether the matrices are conformable with respect to the intended operation. Also, it must be noted whether the matrix operation pertains to matrix elements or to matrices.Addition and Subtraction of Matrix ElementsAddition of Matrix ElementsTo add elements of matrices A and B and store the result as a matrix C,elements of matrix A are added to their corresponding elements in matrix B and stored as elements of matrix C. Obviously, all three matrices must be of the same order or size. Notice that the plus sign in the above equation is enclosed in parentheses to indicate addition of matrix elements, as contrasted with addition of matrices, to be discussed in section to follow. An example of addition of matrix elements is schematized belowand illustrated asSubtraction of Matrix ElementsThe operation of subtracting matrix elements can be schematized asand illustrated asIn sum, the above matrix elements can be add

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