Abstract
Consider the linear substitution
with matrix of coefficients EquationSource% MathType!MTEF!2!1!+- % feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaafa % qabeWadaaabaGaaGymaaqaaiaaigdaaeaacaaIWaaabaGaaGimaaqa % aiaaigdaaeaacaaIWaaabaGaaGimaaqaaiaaicdaaeaacaaIXaaaaa % Gaay5waiaaw2faaaaa!3E8C! ]></EquationSource><EquationSource Format="TEX"><![CDATA[$$\left[ {\begin{array}{*{20}{c}} 1&1&0 \\ 0&1&0 \\ 0&0&1 \end{array}} \right]$$ 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,
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© 1995 Harold M. Edwards
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Edwards, H.M. (1995). Equivalence of Matrices. Reduction to Diagonal Form. In: Linear Algebra. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4446-8_2
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DOI: https://doi.org/10.1007/978-0-8176-4446-8_2
Publisher Name: Birkhäuser, Boston, MA
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