v2009.01.01 - Convex Optimization

706 APPENDIX F. NOTATION AND A FEW DEFINITIONS
A
F(C ∋A)
G(K)
A −1
A †
√
some set (calligraphic ABCDEFGHIJ KLMN OPQRST UVWX YZ)
smallest face (151) that contains element A of set C
generators (2.8.1.2) of set K ; any collection of points and directions
whose hull constructs K
inverse of matrix A
Moore-Penrose pseudoinverse of matrix A
positive square root
A 1/2 and √ A A 1/2 is any matrix √ such that A 1/2 A 1/2 =A .
For A ∈ S n + , A ∈ S
n
+ is unique and √ A √ A =A . [48,1.2] (A.5.2.1)
◦√
D
E
∆ = [ √ d ij ] . (1252) Hadamard positive square root: D = ◦√ D ◦ ◦√ D
elementary matrix
E ij member of standard orthonormal basis for symmetric (52) or symmetric
hollow (67) matrices
1 2 3
⎡ ⎤
· · ·
1
A ij or A(i, j) , ij th entry of matrix A = ⎣ · · · ⎦ 2
· · ·
3
or rank-one matrix a i a T j (4.7)
A i
A(i, :)
A(:, j)
A i:j,k:l
A(ij)
e.g.
no.
i th matrix from a set or i th principal submatrix or i th iterate of A
i th row of matrix A
j th column of matrix A [134,1.1.8]
or A(i:j, k:l) , submatrix taken from i th through j th row and
k th through l th column
A is a function of i and j
exempli gratia, from the Latin meaning for sake of example
number, from the Latin numero