1.4.19 Matrix Transformations

Let the linear operator (widehat {a}) in the space (mathbb {v} _ {3}) of geometric vectors are determined by the effect of display (alpha) on the ends of the radius of the points of the three -dimensional space. Let A - the matrix of the operator (widehat {a}) in the canonical basis (i, j, k). Find your own values and own vectors of the matrix A. Explain how the result is related to the geometric effect of the operator (widehat {a}). Display (Alpha) is designing on the plane (X+Y+Z = 0).