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Eigenvalues and eigenvectors are also called and . λ and may be complex even if is real. The (the ) of = (). is the unit matrix of order .

Definition of an orthogonal matrix. A property of orthogonal matrices. Properties of orthogonal matrices. Orthogonal transformations preserve lengths of vectors. Orthogonal transformations preserve angles.

A special case of (23.1). Valid in general. Valid if + and + are defined. Valid if and are defined. Rule for transposing a Kronecker product. Valid if and exist. and are square matrices, not necessarily of the same order.

Conditions for equilibrium. Equilibrium conditions for the two good case. Comparative statics results for the two good case, = 1, . . . , . Comparative statics results for the good case, = 1, . . . , . See (19.16) for the general formula for the inverse of a square matrix.

The . Properties of the cost function. . *() is the vector * that solves the problem in (25.1). Properties of the conditional factor demand function. . Properties of the .

A property of utility functions that is invariant under every strictly increasing transformation, is called properties are those preserved under strictly increasing transformations. Existence of a continuous utility function. For properties of relations, see (1.16).

Standard neoclassical trade model (2 × 2 ). Two factors of production, and , that are mobile between two output producing sectors and . Production functions are neoclassical (i.e. the production set is closed, convex, contains zero, has free disposal, and its intersection with the positive orthant is empty) and exhibit constant returns to scale. The economy has when both goods are produced.

In an account with interest rate , an amount increases after one period to . Compound interest. (The solution to the difference equation in (28.1).) is called the of . The of an of per period for periods at the interest rate of per period. Payments at the end of each period.

() and (). () is a utility function, is income, or consumption. A characterization of utility functions with constant absolute and relative risk aversion, respectively. and are constants, ≠ 0. Risk aversions for two special utility functions.

Useful sensitivity results for the Black–Scholes model. (The corresponding results for the generalized Black–Scholes model (30.5) are given in Haug (1997), Appendix B.) : cost-of-carry rate of holding the underlying security. = gives the Black–Scholes model. = − gives the Merton stock option model with continuous dividend yield . = 0 gives the Black futures option model. The for the generalized Black–Scholes model.