The Mathematics of Coding: Information, Compression, Error Correction,
... An ordered pair (x, y) is just that, a list of two things in which there is a first thing, here x, and a second thing, here y. Two ordered pairs (x, y) and (x0 , y 0 ) are equal if and only if x = x0 and y = y 0 . The (cartesian) product of two sets A, B is the set of ordered pairs (a, b) where a ∈ ...
... An ordered pair (x, y) is just that, a list of two things in which there is a first thing, here x, and a second thing, here y. Two ordered pairs (x, y) and (x0 , y 0 ) are equal if and only if x = x0 and y = y 0 . The (cartesian) product of two sets A, B is the set of ordered pairs (a, b) where a ∈ ...
Lie Groups and Algebraic Groups
... n × n identity matrix by I (or In if the size of the matrix needs to be indicated); it has entries δij = 1 if i = j and 0 otherwise. Let V be an n-dimensional vector space / V is a linear map we write µ(T ) over F with basis {v1 , . . . , vn }. If T : V for the matrix of T with respect to this basis ...
... n × n identity matrix by I (or In if the size of the matrix needs to be indicated); it has entries δij = 1 if i = j and 0 otherwise. Let V be an n-dimensional vector space / V is a linear map we write µ(T ) over F with basis {v1 , . . . , vn }. If T : V for the matrix of T with respect to this basis ...
Mathematics of Cryptography
... Solution We are looking for the residue r. We can divide the a by n and find q and r. We can then disregard q and keep r. a. Dividing 27 by 5 results in r = 2. This means that 27 mod 5 = 2. b. Dividing 36 by 12 results in r = 0. This means that 36 mod 12 = 0. c. Dividing −18 by 14 results in r = −4. ...
... Solution We are looking for the residue r. We can divide the a by n and find q and r. We can then disregard q and keep r. a. Dividing 27 by 5 results in r = 2. This means that 27 mod 5 = 2. b. Dividing 36 by 12 results in r = 0. This means that 36 mod 12 = 0. c. Dividing −18 by 14 results in r = −4. ...
