A significant application of matrices will be to depict linear transformations, which is, generalizations of linear functions which include file(x) = 4x. By way of example, the rotation of vectors in 3-dimensional space is usually a linear transformation, which may be represented by a rotation matrix R: if v is usually a column vector (a matrix with just one column) describing the posture of some extent in Area, the product Rv can be a column vector describing the place of that time following a rotation.
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The subsequent table shows a variety of 2-by-two matrices with the affiliated linear maps of R2. The blue unique is mapped to the inexperienced grid and shapes.
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