**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Lecture# Linear Applications: Rank and Ciphers

Description

This lecture covers the concept of linear applications, focusing on rank and ciphers. The instructor discusses differentials, gradients, and the properties of various ciphers, emphasizing the importance of understanding the rank of linear transformations and their applications in cryptography.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

In course

Instructor

MATH-213: Differential geometry

Ce cours est une introduction à la géométrie différentielle classique des courbes et des surfaces, principalement dans le plan et l'espace euclidien.

Related concepts (117)

Differentiable function

In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non-vertical tangent line at each interior point in its domain. A differentiable function is smooth (the function is locally well approximated as a linear function at each interior point) and does not contain any break, angle, or cusp. If x0 is an interior point in the domain of a function f, then f is said to be differentiable at x0 if the derivative exists.

Encryption

In cryptography, encryption is the process of encoding information. This process converts the original representation of the information, known as plaintext, into an alternative form known as ciphertext. Ideally, only authorized parties can decipher a ciphertext back to plaintext and access the original information. Encryption does not itself prevent interference but denies the intelligible content to a would-be interceptor. For technical reasons, an encryption scheme usually uses a pseudo-random encryption key generated by an algorithm.

Linear combination

In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants). The concept of linear combinations is central to linear algebra and related fields of mathematics. Most of this article deals with linear combinations in the context of a vector space over a field, with some generalizations given at the end of the article.

Semi-differentiability

In calculus, a branch of mathematics, the notions of one-sided differentiability and semi-differentiability of a real-valued function f of a real variable are weaker than differentiability. Specifically, the function f is said to be right differentiable at a point a if, roughly speaking, a derivative can be defined as the function's argument x moves to a from the right, and left differentiable at a if the derivative can be defined as x moves to a from the left.

Differentiable manifold

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus. Any manifold can be described by a collection of charts (atlas). One may then apply ideas from calculus while working within the individual charts, since each chart lies within a vector space to which the usual rules of calculus apply. If the charts are suitably compatible (namely, the transition from one chart to another is differentiable), then computations done in one chart are valid in any other differentiable chart.

Related lectures (961)

Meromorphic Functions & DifferentialsMATH-410: Riemann surfaces

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Differential Calculus: Applications and RemindersMATH-213: Differential geometry

Covers differential calculus applications and reminders, emphasizing the importance of differentiability in mathematical analysis.

Matrix Similarity and Diagonalization

Explores matrix similarity, diagonalization, characteristic polynomials, eigenvalues, and eigenvectors in linear algebra.

Differential Forms on ManifoldsMATH-410: Riemann surfaces

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Differential Forms IntegrationMATH-410: Riemann surfaces

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.