Modular inverses of 2x2 matrices
[DOC File]Caesar’s Cipher - TI89
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Example5: The set of 2x2 matrices with real coefficients. Not every 2x2 matrix has an inverse matrix, namely the ones with a determinant =0. Example6: The set of all continuous functions f having the real numbers as the domain and the range.
[DOC File]Chapter
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Images are considered to be N x M matrices, where N is the number of pixel rows and M is the number of pixel columns of the images. The independent variables x and y are used as indices refering to a single pixel in the image matrix. ... The inverse of this 2x2 matrix is easy and is listed in [].The final inverse affine transformation is thus ...
[DOC File]Advanced Discrete Exam 2 Name
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2(2 matrices over Z (d) ring without identity that is not commutative. 2(2 matrices over E. 11. (a) Define: a . primitive root. of prime number p. An integer with p-1 distinct powers mod p (b) Complete the description below of the mechanics of the ElGamal Cryptosystem. The receiver chooses a prime p, a primitive root ( of p, and a secret ...
[DOC File]MA 120-50 FA 05 Supplementary Notes
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2.3 Modular arithmetic 51. 2.4 Congruence mod n 53. 2.5 Getting Ready for Induction 55 ... inverses 115. 5.6 Image and pre-image 116. 5.7 Permutations 125 ... we might want to shorten a proof by replace 2x2 – 4x + 1 by a single variable. As long as that variable . has not yet been used in the proof, this is OK; we call it “introduction of a ...
[DOC File]GROUPS, RINGS AND FIELDS
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Thus, the rules for ordinary arithmetic involving addition, subtraction, and multiplication carry over into modular arithmetic. Modular arithmetic operations (CONT 1) Table 4.1 introduces arithmetic modulo 8. We see that not for all elements exist multiplicative inverses (for 2, 4, 6). Properties of modular arithmetic. Let Zn ={0,1,..,n-1}.
[DOC File]Discrete Mathematics - MGNet
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Proof: Since gcd(a,m) = 1, (s,t(Z(1 = sa+tb). Hence, sa=tb ( 1 (mod m). Since tm ( 0 (mod m), it follows that sa ( 1 (mod m). Thus, s is the inverse of a modulo m. The uniqueness argument is made by assuming there are two inverses and proving this is a contradiction. Systems of linear congruences are used in large integer arithmetic.
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