TY - JOUR

T1 - Letters to the Editor

T2 - Chaganty, N. R. (1993), "Comment," the American Statistician, 47,158: Comments by Bancroft and Neudecker and Liu with response by Chaganty and Vaish

AU - Bancroft, Diccon R. E.

AU - Neudecker, Heinz

AU - Liu, Shuangzhe

AU - Chaganty, Narasinga Rao

AU - Vaish, A. K.

AU - Nemenyi, Peter

AU - Murray Lindsay, R.

AU - Ehrenberg, Andrew S. C.

AU - Laubscher, Nico F.

AU - Jones, Michael C.

PY - 1994

Y1 - 1994

N2 - Chaganty (1993), in a letter to the editor commenting on an article by Olkin (1992), offered as a theorem a version of the Cauchy-Schwartz inequality. When B is a symmetric nonnegative definite matrix with Moore-Penrose inverse B+, it has a symmetric nonnegative definite square root C with Moore-Penrose inverse C+. This follows from the singular value decomposition of B. The matrices BB', B+B, CC', and C+C are all equal to PB, the projection matrix into M(B), the column space of B. Apply the Cauchy-Schwartz inequality to the n x 1 vectors Cx', C+b' to obtain.

AB - Chaganty (1993), in a letter to the editor commenting on an article by Olkin (1992), offered as a theorem a version of the Cauchy-Schwartz inequality. When B is a symmetric nonnegative definite matrix with Moore-Penrose inverse B+, it has a symmetric nonnegative definite square root C with Moore-Penrose inverse C+. This follows from the singular value decomposition of B. The matrices BB', B+B, CC', and C+C are all equal to PB, the projection matrix into M(B), the column space of B. Apply the Cauchy-Schwartz inequality to the n x 1 vectors Cx', C+b' to obtain.

M3 - Letter

SN - 0003-1305

VL - 48

SP - 351

EP - 354

JO - American Statistician

JF - American Statistician

IS - 4

ER -