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where | | denotes a determinant (see eqns (B26 B27))and i, j, and k are unit vectors pointing along the principal axes of the reference frame It is sometimes convenient, see for example Section 255, to express the vector product of eqn (B13) in the matrix form u v = Uv where 0 U = u3 u2 u3 0 u1 u2 u1 0 (B14)

(B15)

1:

This skew symmetric form of u is convenient in analysis The equivalence expressed in eqn (B14) will be denoted U = [u ] The vector product has the following properties: = = = = = = (u v) (w z) = u u u v u (v w) u (v w) u (v w) 0 v u (u v) w (u w) v (u v) w v (w u) w (u v) (u w) (v z) (v w) (u z) (B16) (B17) (B18) (B19) (B20) (B21) (B22)

Using eqn (B17) and the U = [u ] notation, we can derive the following useful formula: u v = Uv (B23) (B24)

Exadata Storage Server Cells (7)

$ 1,200 900 600 300 0 300 600 900 1,200 1013 1272 1532 1791 2050 2309 2568 2828 3087 Profit/loss by change in HD common price

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where V = [v ] is the skew symmetric matrix corresponding to v as de ned in eqn (B15) The trace of square matrix A Rn n is the sum of its diagonal elements

T r(A) =

Database Server Nodes (4) InfniBand Switch (2) Database Server Nodes (4)

(B25)

The trace is not de ned unless its argument is square The trace has several convenient properties: 1 T r A = T r(A),

FIGURE 1-1

2 T r (A + B) = T r(A) + T r(B), 3 T r(ABC) = T r(BCA) = T r(CAB) if all required matrix products are well de ned, 4 T r(vv ) = T r(v v) = v 2 , 5 T r(A) =

to the outright stock purchase because of the $233 premium paid for the option as shown in Figure 41 However, once the option is rmly in the money, the value of the option will keep pace with the underlying at a 1 to 1 ratio once the delta of the option is 100 You can see the limited risk of the option versus the underlying as the call option loss atlines while the underlying price loss continues to deepen

Given vectors ui Rn for i = 1, , m, the vectors are linearly dependent if m there exists i R, not all zero, such that i=1 i ui = 0 If the summation is only zero when all i = 0, then the set of vectors is linearly independent A set of m > n vectors in Rn is always linearly dependent A set of n vectors ui Rn , i = 1, , n can be arranged as a square matrix U = [u1 , u2 , , un ] Rn n Note that a matrix can always be decomposed into its component column (or row) vectors The rank of a matrix, denoted rank(U), is the number of independent column (or row) vectors in the matrix If this set of vectors is linearly independent (ie, rank(U) = n), then we say that the matrix U is nonsingular (or of full rank) A convenient tool for checking whether a square matrix is nonsingular is the determinant The determinant of A Rn n , denoted |A| or det(A),

The specifics of this hardware will continue to change over time But the fundamental balanced design concepts continue with each subsequent release of the product As new designs emerge, capacities and performance levels continue to improve across these key components in a balanced fashion

(B26)

(B27)

Though understanding the hardware concepts is important, it is equally important to understand the implications of Oracle s software integration to this platform Oracle s platform support includes the operating system, Oracle Enterprise Linux, as the foundation for the database server nodes and Exadata Storage Server cells As an alternative, Oracle also offers the Solaris 11 operating system for the database server nodes Upon this platform, Oracle tightly integrates Oracle Database 11 g Enterprise Edition and extends database functionality into storage with the Exadata Storage Server Software Other Oracle database software components on the platform that are central to a typical deployment are RAC and the Oracle Partitioning Option

For a square matrix A, the cofactor associated with akj is ckj = ( 1)k+j Mkj (B28)

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