Linear Algebra pp 104-111 | Cite as

Matrices and linear transformations

  • Larry Smith
Part of the Undergraduate Texts in Mathematics book series (UTM)


We come now to the connecting link between linear transformations and matrices. Our approach will be to consider first the case of a linear transformation
$$ {\text{T}}:{R^3} \to {R^3} $$
in some detail and then abstract the salient features to the general case. Let us therefore suppose given a fixed linear transformation \( {\text{T}}:{R^3} \to {R^3} \). As usual we will denote by E1, E2, E3 the standard basis vectors (1,0,0), (0, 1, 0), (0, 0, 1) in ℝ3. Let
$${\text{T}}({{\text{E}}_1}){\text{ = }}({a_{11}},{a_{21}},{a_{31}}){\text{T}}({{\text{E}}_2}){\text{ = }}({a_{12}},{a_{22}},{a_{32}}){\text{T}}({{\text{E}}_3}){\text{ = }}({a_{13}},{a_{23}},{a_{33}})$$


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Copyright information

© Springer-Verlag New York Inc. 1984

Authors and Affiliations

  • Larry Smith
    • 1
  1. 1.Mathematisches InstitutUniversität GöttingenGöttingenWest Germany

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