Equivalence of Matrices. Reduction to Diagonal Form
Consider the linear substitutionwith matrix of coefficients This substitution is easy to invert. That is, while the substitution expresses x, y, and z in terms of a, b, and c, one can easily express a, b, and c in terms of x, y, and z; merely subtract the second equation of (1) from the first to find
or, in the format of a linear substitution,
KeywordsIdentity Matrix Linear Algebra Diagonal Entry Nonzero Entry Successive Pair
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© Harold M. Edwards 1995