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Course# MATH-111(pi): Linear algebra (flipped classroom)

Summary

L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et ses applications. Cette classe pilote est donné sous forme inversée.

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Related courses (32)

Related MOOCs (10)

Related concepts (48)

L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et ses applications.

L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et ses applications.

L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et ses applications.

L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et ses applications.

L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et ses applications.

Algebra (part 1)

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.

Algebra (part 1)

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.

Algebra (part 2)

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.

Pauli matrices

In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices which are Hermitian, involutory and unitary. Usually indicated by the Greek letter sigma (σ), they are occasionally denoted by tau (τ) when used in connection with isospin symmetries. These matrices are named after the physicist Wolfgang Pauli. In quantum mechanics, they occur in the Pauli equation which takes into account the interaction of the spin of a particle with an external electromagnetic field.

Gamma matrices

In mathematical physics, the gamma matrices, also called the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra It is also possible to define higher-dimensional gamma matrices. When interpreted as the matrices of the action of a set of orthogonal basis vectors for contravariant vectors in Minkowski space, the column vectors on which the matrices act become a space of spinors, on which the Clifford algebra of spacetime acts.

Scalar multiplication

In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract algebra). In common geometrical contexts, scalar multiplication of a real Euclidean vector by a positive real number multiplies the magnitude of the vector—without changing its direction. The term "scalar" itself derives from this usage: a scalar is that which scales vectors.

Inner product space

In mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product. The inner product of two vectors in the space is a scalar, often denoted with angle brackets such as in . Inner products allow formal definitions of intuitive geometric notions, such as lengths, angles, and orthogonality (zero inner product) of vectors. Inner product spaces generalize Euclidean vector spaces, in which the inner product is the dot product or scalar product of Cartesian coordinates.

Definite matrix

In mathematics, a symmetric matrix with real entries is positive-definite if the real number is positive for every nonzero real column vector where is the transpose of . More generally, a Hermitian matrix (that is, a complex matrix equal to its conjugate transpose) is positive-definite if the real number is positive for every nonzero complex column vector where denotes the conjugate transpose of Positive semi-definite matrices are defined similarly, except that the scalars and are required to be positive or zero (that is, nonnegative).

Lectures in this course (14)

Linear Equations: Solutions and ConditionsMATH-111(pi): Linear algebra (flipped classroom)

Explores linear equations, infinity of solutions, and incompatible systems.

Linear Algebra: Basis Change and MatricesMATH-111(pi): Linear algebra (flipped classroom)

Explores basis change in linear algebra and the role of matrices.

Orthogonally Diagonalizable MatricesMATH-111(pi): Linear algebra (flipped classroom)

Explores orthogonally diagonalizable matrices, eigenvectors, bases, and matrix properties.

Linearly Dependent VectorsMATH-111(pi): Linear algebra (flipped classroom)

Explores linearly dependent vectors in three-dimensional space and their impact on forming a basis.

Matrix Operations and Vector SpacesMATH-111(pi): Linear algebra (flipped classroom)

Covers elementary matrix operations and vector spaces, including properties and conditions for invertibility.