Showing 131 - 140 of 167
results
Décomposition et calcul matriciel par blocs
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook introduces block partitions of matrices and derives blockwise addition, scalar multiplication, and matrix multiplication. Examples and exercises show how compatible partitions simplify matrix calculations.
- Block matrix
- Matrix multiplication
- Matrix partition
Multiplication de matrices
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook defines matrix multiplication through row-column products and explains the required dimension compatibility. Students compute products and investigate the main algebraic properties of matrix multiplication.
- Matrix multiplication
- Matrix dimension
- Row-column product
Matrices carrées et matrices inversibles
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook defines square, identity, and invertible matrices and introduces the matrix inverse. Examples and exercises show how inverses behave and how to determine candidate inverse matrices.
- Square matrix
- Invertible matrix
- Matrix inverse
- Identity matrix
Application de la décomposition LU aux systèmes linéaires
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook uses a factorization A=LU to solve linear systems through two successive triangular systems. Students practice forward and backward substitution and compare the workflow with direct elimination.
- LU decomposition
- Linear system
- Forward substitution
- Backward substitution
Matrices élémentaires et opérations sur les lignes
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook defines the three elementary row operations and their associated elementary matrices. It shows how left multiplication performs row operations and relates elementary matrices to invertibility.
- Elementary matrix
- Elementary row operation
- Matrix multiplication
- Invertible matrix
Systèmes homogènes et base de l'espace des solutions
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook shows that the solution set of Ax=0 is a vector subspace and relates its dimension to the number of free variables. Students find bases of null spaces from row-echelon systems.
- Homogeneous system
- Null space
- Free variable
- Basis
Coordonnées par rapport à une base
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook defines the coordinate vector of an element relative to an ordered basis and explains its uniqueness. Exercises compute coordinates in several vector spaces and reconstruct vectors from coordinate columns.
- Coordinate vector
- Ordered basis
- Change of basis
- Linear combination
Rang-colonne et compatibilité des systèmes linéaires
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook characterizes the consistency of a linear system by comparing the column ranks of its coefficient and augmented matrices. Step-by-step exercises use the rank condition to determine and solve compatible systems.
- Matrix rank
- Column space
- Consistent system
- Augmented matrix
Dépendance et indépendance linéaire
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook defines linearly dependent and independent families and develops criteria based on nontrivial linear combinations. Propositions and exercises help students detect redundant vectors in finite families.
- Linear independence
- Linear dependence
- Linear combination
Rang-ligne et rang-colonne d'une matrice
- Professor Simone Deparis
- CourseMATH-111
- Kernel Python3
- Type Interactive textbook
- Language English
- DescriptionThis notebook defines row rank and column rank as dimensions of the corresponding matrix subspaces and establishes their equality. Students compute ranks using row reduction, pivot rows, and pivot columns.
- Matrix rank
- Row space
- Column space
- Pivot