MAT223H1 Chapter Notes - Chapter 6.4: Invertible Matrix, Diagonalizable Matrix, Diagonal Matrix
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Let"s remember the de nition of a diagonal matrix. We say a matrix d is diagonal if it has the form. 2. 1 finding d let a be an n n matrix with linearly independent eigen- vectors u1, . Since b is a basis for rn, then every vector x rn has a unique set of scalars c1, . Diagonal matrices are very desirable because the sim- plify the solutions of systems of equations to a minimum complexity. In effect, the solution of xb = c1u1 + . , n are the eigenvalues of a associated with u1, . Ax = a ciui ciaui ci iui i=1 i=1 i=1 n(cid:88) n(cid:88) n(cid:88) In this section we study conditions and procedures to turn a matrix into its diagonal form. An n n a is diagonalizable if there exists n n matrices d and p , with d diagonal and p invertible, such that.
