“JUST THE MATHS” SLIDES NUMBER 8.1 VECTORS 1
... 8. A vector whose magnitude is 1 is called a “unit vector”. The symbol ab denotes a unit vector in the same direction as a. A vector whose magnitude is zero is called a “zero vector” and is denoted by O or O. It has indeterminate direction. 9. Two (free) vectors a and b are said to be “equal” if th ...
... 8. A vector whose magnitude is 1 is called a “unit vector”. The symbol ab denotes a unit vector in the same direction as a. A vector whose magnitude is zero is called a “zero vector” and is denoted by O or O. It has indeterminate direction. 9. Two (free) vectors a and b are said to be “equal” if th ...
November 20, 2013 NORMED SPACES Contents 1. The Triangle
... There are other matrix norms easier to calculate than the operator norm (9), for example kM k1 = maxi,j |Mij | (but it is not compatible with matrix multiplication). Since Mn (F ) is finite dimensional, all the norms are equivalent. Therefore, to check convergence, any of the norms can be used. Depe ...
... There are other matrix norms easier to calculate than the operator norm (9), for example kM k1 = maxi,j |Mij | (but it is not compatible with matrix multiplication). Since Mn (F ) is finite dimensional, all the norms are equivalent. Therefore, to check convergence, any of the norms can be used. Depe ...
Quotient spaces defined by linear relations
... Proof. A subset F o f Yis open if and only if/~ ^[V) is open inX. Tiierefore, if U is an open subset of X, t h e n / ( l / ) is open in У since/"^(/(t/)) = U + /~^(0) is open in X. This shows that / is an open mapping. Now, it is easy to see that the vector space operations in Y are continuous. (Ob ...
... Proof. A subset F o f Yis open if and only if/~ ^[V) is open inX. Tiierefore, if U is an open subset of X, t h e n / ( l / ) is open in У since/"^(/(t/)) = U + /~^(0) is open in X. This shows that / is an open mapping. Now, it is easy to see that the vector space operations in Y are continuous. (Ob ...
The Logic of Recursive Equations
... displayed explicitly, e.g., E[M/x*l] denotes the result of substituting the FLROterm Mi for xi, for each xi in the sequence x*. Further, if the term E has been written as E(xl,. . , Xn), displaying (some of) its free variables, then the substitution E[M/lZ] may also be written E (M1, . . ., M,,) . F ...
... displayed explicitly, e.g., E[M/x*l] denotes the result of substituting the FLROterm Mi for xi, for each xi in the sequence x*. Further, if the term E has been written as E(xl,. . , Xn), displaying (some of) its free variables, then the substitution E[M/lZ] may also be written E (M1, . . ., M,,) . F ...
2010 competition solutions
... Since m and k are both integers, and 2011 is a prime number, there are only 4 possible combinations for which the above equation holds: m = 2011; k – 1 = 1 x = 4022; y = 4022 m = –2011; k – 1 = –1 x = 0; y = 0 (reject) m = 1; k – 1 = 2011 x = (2011)(2012) = 4046132; y = 2012 m = –1; k – 1 = –2 ...
... Since m and k are both integers, and 2011 is a prime number, there are only 4 possible combinations for which the above equation holds: m = 2011; k – 1 = 1 x = 4022; y = 4022 m = –2011; k – 1 = –1 x = 0; y = 0 (reject) m = 1; k – 1 = 2011 x = (2011)(2012) = 4046132; y = 2012 m = –1; k – 1 = –2 ...
Multilinear Representations for Ordinal Utility
... for some functions a,, a*. Using this equation to replace o$, and repeating.for vf2 and u& we see that only three two-dimensional functions are required, and that, with some redefinition, the equations may be written as in the statement of the lemma. The case n = 4 is more tedious, but is also found ...
... for some functions a,, a*. Using this equation to replace o$, and repeating.for vf2 and u& we see that only three two-dimensional functions are required, and that, with some redefinition, the equations may be written as in the statement of the lemma. The case n = 4 is more tedious, but is also found ...
Covariance - KSU Faculty Member websites
... covariance equal to 4.00. This value is equal to the value of the covariance coefficient computed from the formula expressed in deviation scores computed previously. Lack of Upper and LowerLimits The coefficient of covariance has no upper or lower limits. As will be seen later, this indeterminacy i ...
... covariance equal to 4.00. This value is equal to the value of the covariance coefficient computed from the formula expressed in deviation scores computed previously. Lack of Upper and LowerLimits The coefficient of covariance has no upper or lower limits. As will be seen later, this indeterminacy i ...
Math 8 HW 19 Solving Proportions
... $5 for 4 loaves of bread 6) Write a proportion that could be used to solve for the given above variable and solve for that same variable. ...
... $5 for 4 loaves of bread 6) Write a proportion that could be used to solve for the given above variable and solve for that same variable. ...
