Translation and analysis of words by ChatGPT artificial intelligence
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transposition basis - translation to russian
математика
базис транспозиций
![This picture illustrates the [[standard basis]] in '''R'''<sup>2</sup>. The blue and orange vectors are the elements of the basis; the green vector can be given in terms of the basis vectors, and so is [[linearly dependent]] upon them.](https://commons.wikimedia.org/wiki/Special:FilePath/Basis graph (no label).svg?width=200 "This picture illustrates the [[standard basis]] in '''R'''<sup>2</sup>. The blue and orange vectors are the elements of the basis; the green vector can be given in terms of the basis vectors, and so is [[linearly dependent]] upon them.")
![[−1, 1]<sup>''n''</sup>}} as a function of dimension, ''n''. Boxplots show the second and third quartiles of this data for each ''n'', red bars correspond to the medians, and blue stars indicate means. Red curve shows theoretical bound given by Eq. (1) and green curve shows a refined estimate.<ref name = "GorbanTyukin2016"/>](https://commons.wikimedia.org/wiki/Special:FilePath/Random almost orthogonal sets.png?width=200 "[−1, 1]<sup>''n''</sup>}} as a function of dimension, ''n''. Boxplots show the second and third quartiles of this data for each ''n'', red bars correspond to the medians, and blue stars indicate means. Red curve shows theoretical bound given by Eq. (1) and green curve shows a refined estimate.<ref name = \"GorbanTyukin2016\"/>")
математика
векторный базис
математика
упорядоченный базис
Wikipedia
In cryptography, a transposition cipher (also known as a permutation cipher) is a method of encryption which scrambles the positions of characters (transposition) without changing the characters themselves. Transposition ciphers reorder units of plaintext (typically characters or groups of characters) according to a regular system to produce a ciphertext which is a permutation of the plaintext. They differ from substitution ciphers, which do not change the position of units of plaintext but instead change the units themselves. Despite the difference between transposition and substitution operations, they are often combined, as in historical ciphers like the ADFGVX cipher or complex high-quality encryption methods like the modern Advanced Encryption Standard (AES).
