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 -