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. Author manuscript; available in PMC: 2018 Sep 24.

Published in final edited form as: Ann Stat. 2018 Jun 27;46(4):1742–1778. doi: 10.1214/17-AOS1601

Table 1:

Systematic notation for the 26 loss functions considered in this paper.

	MatrixNorm
Pivot	Frobenius	Operator	Nuclear
A − B	L^F,1	L^O,1	L^N,1
A⁻¹ − B⁻¹	L^F,2	L^O,2	L^N,2
A⁻¹B − I	L^F,3	L^O,3	L^N,3
B⁻¹A − I	L^F,4	L^O,4	L^N,4
A⁻¹ B + B⁻¹ A − 2I	L^F,5	L^O,5	L^N,5
A^−1/2 BA^−1/2 − I	L^F,6	L^O,6	L^N,6
Log(A^−1/2 BA^−1/2)	L^F,7	L^O,7	L^N,7
	Statistical Measures
	St	Ent	Div
Stein	L^st	L^ent	L^div
Affinity	L^aff
Fréchet	L^fre