The case " p " = & infin; yields the spectral norm, which is the matrix norm induced by the vector 2-norm ( see above ).
12.
The convergence criteria of the power series then apply, requiring \ Vert \ eta A ^ {-1 } B \ Vert to be sufficiently small under the appropriate matrix norm.
13.
This notation can be ambiguous since it is also used for certain matrix norms and for the absolute value " !-- talk ) 17 : 09, 23 December 2008 ( UTC)
14.
Additionally, in the case of square matrices ( thus, ), some ( but not all ) matrix norms satisfy the following condition, which is related to the fact that matrices are more than just vectors:
15.
Also, if A is a matrix, | A | is used to denote the determinant of | A |, even though det ( A ) is usually preferred, because | A | may be better used to denote a matrix norm.
16.
Here P _ { A _ j } denotes the orthogonal projection on the space spanned by the standard unit vectors corresponding to the elements so that the matrix of P _ { A _ j } T P _ { A _ j } is obtained from the matrix of T by replacing all rows and columns that don't correspond to the indices in A _ j The matrix norm \ | . \ | is the spectral norm, i . e . the operator norm with respect to the Euclidean norm
