18.03 Lecture Notes - Row And Column Vectors, Linear Combination, Identity Matrix
Document Summary
Eigenvalues and eigenvectors: linear algebra, ray solutions, eigenvalues, eigenvectors, initial values. Recall [a b ; c d] [x ; y] = x[a ; c] + y[b ; d] : A matrix times a column vector is the linear combination of the columns of the matrix weighted by the entries in the column vector. One way is for x = 0 = y. If [a ; c] and [b ; d] point in different directions, this is the only way. But if they lie along a single line, we can find x and y so that the sum cancels. Write a = [a b ; c d] and u = [x ; y] , so we have been thinking about a u = 0 as an equation for u . We get a nonzero solution [x ; y] exactly when the slopes of the vectors.
