Applied Mathematics 1411A/B Lecture Notes - Lecture 16: Transformation Matrix, Row And Column Vectors, Elementary Matrix
12 Mar 2015
School
Department
Professor
Document Summary
Recall: last day, we said that the standard matrix for a transformation can be found using . Example: find the standard matrix for the linear operator. 2 vector onto the x-axis, then contracts that image by a factor of 5. Definition: if we have succession by finding the composition of tb with ta, denoted by x x to produce a transformation from rn to rm. 2 x y , then rotates that image by. Example: find the standard matrix for the linear operator vector versus the line dilates that image by a factor of 3. R is said to be one-to-one if t maps n. Definition: a linear transformation distinct vectors (points) in rn into distinct vectors (points) in rm. Example: determine if the following transformation is one-to-one. R is multiplication by a, then the: rotation, projection nn matrix and. Theorem: if a is an following statements are equivalent: a is invertible, the range of at is.
