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linear transformation |
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linear transformationIn mathematics, a rule for changing one geometric figure (or matrix or vector) into another using a formula with a specified format. The format must be a linear combination, in which the original components (e.g., the x and y coordinates of each point of the original figure) are changed via the formula ax + by to produce the coordinates of the transformed figure. Examples include flipping the figure over the x or y axis, stretching or compressing it, and rotating it. Every such transformation has an inverse, which undoes its effect. linear transformation [′lin·ē·ər ‚tranz·fər′mā·shən] (mathematics) A functionTdefined in a vector spaceEand having its values in another vector space over the same field, such that if ƒ andgare vectors inE,andcis a scalar, thenT(ƒ +g) =Tƒ +TgandT(cƒ) =c(Tƒ). Also known as homogeneous transformation; linear function; linear operator.
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The book provides guidance not only on systems of linear equations and matrix algebra but also on the often-harder-to-grasp topics of vector spaces, linear transformations, determinants, and eigenvector problems. Application: Linear transformation simplifies data analysis. |
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