Linear Transformation
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A function from one vector space to another. If bases are chosen for the vector spaces, a linear transformation can be given by a matrix.
Linear transformation is a college-level concept that would be first encountered in a linear algebra course.
Prerequisites
| Matrix: | A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, for every linear transformation, there exists exactly one corresponding matrix, and every matrix corresponds to a unique linear transformation. The matrix is an extremely important concept in linear algebra. |
| Vector: | (1) In vector algebra, a vector mathematical entity that has both magnitude (which can be zero) and direction. (2) In topology, a vector is an element of a vector space. |
| Vector Space: | A vector space is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space. |