COROLLARY 2.3. lf Tis the product o

COROLLARY 2.3. lf Tis the product of two nonnegative matrices, so are T, and T,. Proof. By Theorem 2.2, T is similar to a nonnegative diagonal matrix. It is easily seen that Tl and T2 are also similar to diagonal matrices and that their eigenvalues are nonnegative. Hence, by Theorem 2.2 again, they are products of two nonnegative matrices. n 3. THREE NONNEGATIVE MATRICES In this section, we will give a sufficient condition, in terms of Ballantine’s characterization of the products of three positive matrices, for a matrix to be

結果 (中文) 1:

2.3 的必然结果。lf Tis 两个非负矩阵的乘积，所以是 T 和 T。证明。由定理 2.2 T 是类似于一个非负的对角矩阵。Tl 和 T2 是也相似对角矩阵和其特征值都是非负是显而易见的。因此，由定理 2.2 再一次，他们是两个非负矩阵的产品。n 3。本节中的三个非负矩阵，我们会给一个充分的条件，在产品的三个积极的矩阵，矩阵是百龄坛的表征

結果 (中文) 3:

推论2.3。如果这两个非负矩阵的产品，所以T，T，。证明。由定理2.2，吨是类似于一个非负对角矩阵。很容易看出，T1和T2也类似于对角矩阵和特征值是非负。因此，通过定理2.2，他们是双非负矩阵的乘积。3。本节中的三个非负矩阵，我们将给出一个充分的条件，在百龄坛的产品的三个正矩阵的特性，为一个矩阵为