Henri Cartan was a prominent French mathematician, born on July 8, 1904, and he passed away on August 13, 2008. He was known for his contributions to several areas of mathematics, including topology, algebraic topology, and homological algebra. Cartan was a key figure in the development of sheaf theory and cohomology, and he played an important role in the establishment of algebraic geometry and the theory of complex spaces.

An Introduction to Tensors and Group Theory for Physicists by Nadir Jeevanjee (2011) shows that this is a tensor that represents the volume of a parallelepiped.

It takes as input three vectors, and outputs one real number, the volume. And it is linear on each vector. This perfectly satisfied the definition of a tensor of order (3,0).

Given a basis $(e_i,e_j,e_k)$ and a function that return the volume of a parallelepiped given by three vectors $V(v_1,v_2,v_3)$, ${\epsilon }_{ikj}=V(e_i,e_j,e_k)$.

Name origin: likely because it "determines" if a matrix is invertible or not, as a matrix is invertible iff determinant is not zero.

Since a matrix $M$ can be seen as a linear map $f_M(\vec{x})$, the product of two matrices $MN$ can be seen as the composition of two linear maps:One cool thing about linear functions is that we can easily pre-calculate this product only once to obtain a new matrix, and so we don't have to do both multiplications separately each time.

Set of eigenvalues of a linear operator.

Faugère's F4 and F5 algorithms are important algorithms in computer algebra for solving systems of polynomial equations and performing computations in polynomial rings. They are particularly useful in the context of Gröbner bases, which are a fundamental tool for solving problems in algebraic geometry, coding theory, cryptography, and other areas requiring polynomial manipulation.

The Cosmic Censorship Hypothesis is a conjecture in general relativity proposed by physicist Roger Penrose in the 1960s. It primarily deals with the nature of singularities that can form in spacetime due to gravitational collapse.

Pollen DNA barcoding is a molecular technique used to identify and categorize different types of pollen grains based on their genetic material. It leverages the principles of DNA barcoding, which involves sequencing a short, standardized region of DNA that is unique to each species. By analyzing these genetic sequences, researchers can create a "barcode" that distinguishes one species from another.

Sturm's theorem, or Sturm's sequence, is a mathematical result concerning the number of real roots of a polynomial within a given interval. Named after the French mathematician Jacques Charles François Sturm, it provides a systematic way to count the distinct real roots of a polynomial by using Sturm sequences.

The development of computers has progressed significantly over the decades, with various milestones marking the introduction of key concepts, technologies, and advancements. Here's a brief overview of computer-related introductions by millennium: ### 20th Century (1900s - 1999) - **1940s - 1950s: Early Computers** - **1943-1944**: Colossus, the first programmable digital computer, was developed for code-breaking during World War II.

Computer science educators are individuals who teach and promote the understanding of computer science concepts, theories, and practices. They can work in a variety of settings, including primary and secondary schools, colleges, universities, and online platforms. Their primary goal is to equip students with the knowledge and skills necessary to understand computer science fundamentals, coding, algorithms, data structures, software development, and other related topics.

Pedro Domingos is a computer scientist and a professor at the University of Washington, known for his work in machine learning, data mining, and artificial intelligence. He has made significant contributions to the field, including research on algorithms and techniques that advance the understanding and application of machine learning. Domingos is also the author of the book "The Master Algorithm," which discusses the concept of a universal learning algorithm that can learn from any type of data.

"Anna Becker" could refer to a number of different people or concepts, as it is a relatively common name. Without additional context, it’s difficult to provide a precise answer. It could refer to: 1. A person, such as a public figure, artist, or professional in a certain field. 2. A fictional character in a book, movie, or TV show. 3. A historical figure or someone notable in a particular domain.

Marie-Louise Saboungi is not a widely recognized individual or term as of my last update in October 2023. It could refer to a specific person or character within a niche context, such as literature, art, or academia, but additional information would be necessary to provide a definitive answer.

As of my last update in October 2021, Michael S. Montalbano does not appear to be a widely recognized public figure or historical figure. If he is a person who has gained prominence after this date, I wouldn't have that information. Could you provide more context or details regarding who he is or what field he is associated with?