Linear Systems
 
Overview on linear systems
0.00%
Row Reduction
0.00%
Plan for Row Reduction
0.00%
Notation for Row Operations
0.00%
Algorithm for Row Reduction
0.00%
Matrices
0.00%
Matrix Operations and Matrix Algebra
0.00%
Matrix Equations
0.00%
The Superposition Principle
0.00%
Elementary Matrices
0.00%
Vector Spaces and Linear Transformations
 
Vector Spaces
0.00%
The vector space ℝn
0.00%
Definition of a vector space
0.00%
Subspaces
0.00%
Linear combinations and linear independence
0.00%
Constructing and Describing Vector Spaces and Subspaces
0.00%
Spanning sets, row spaces, and column spaces
0.00%
Nullspaces
0.00%
Range
0.00%
Bases and dimension
0.00%
Coordinate systems
0.00%
Vector spaces over ℂ
0.00%
Linear Transformations
0.00%
Definition
0.00%
Matrix representations of transformations
0.00%
Change of basis
0.00%
Vector spaces of linear transformations
0.00%
Eigenvalues and Eigenvectors
 
The Determinant
0.00%
Cofactor expansion
0.00%
Combinatorial definition
0.00%
Properties of the determinant
0.00%
Eigenvalues and Eigenvectors
0.00%
Definition
0.00%
Eigenspaces
0.00%
The characteristic polynomial
0.00%
Direct sum decomposition
0.00%
Properties of Eigenvalues and Eigenvectors
0.00%
Similarity and diagonalization
0.00%
Complex eigenvalues and eigenvectors
0.00%
Geometric versus algebraic multiplicity
0.00%
Shur’s Theorem
0.00%
Normal matrices
0.00%
Generalized eigenvectors
0.00%
Inner Product Spaces
 
Inner Products on ℝn
0.00%
The dot product in ℝn
0.00%
Symmetric bilinear pairings on ℝn
0.00%
Orthogonal vectors and subspaces in ℝn
0.00%
Orthonormal vectors and orthogonal matrices
0.00%
Projections and Least-squares Approximations
0.00%
Projection onto 1-dimensional subspaces
0.00%
Gram-Schmidt orthogonalization
0.00%
Least-squares approximations
0.00%
Least-squares solutions and the Fundamental Subspaces theorem
0.00%
Applications of least-squares solutions
0.00%
Projection onto a subspace
0.00%
Polynomial data fitting
0.00%
Complex inner product spaces
0.00%
The complex scalar product in ℂn
0.00%
Conjugate-symmetric sesquilinear pairings on ℂn, and their representation
0.00%
Unitary matrices
0.00%
Singular Values
 
Singular value decomposition
0.00%

Overall
0%

https://ximera.osu.edu/certificate/H4sIAAAAAAACAyXMOwvCMBQF4L8SMtvmYdvYbE4iONbFLUmvGkwbyAMK4n830eFy4PCd%2B8arWgBLfMoQE7pGCHiHcw2JN7tAUK2PuYU5k9pGMggtxL1j2mg4sHmgSvQdG0yZzSrVV5zyvqG84XRio2S9ZPuW8fFWhPE5xGqIsyuooNwDdFAkwZa0969Ckk2uiulpI0LncpcfRej4x8VE40Mx9PMFBEqPRr8AAAA%3D/cy1wkJWTu5axoEP%2Fhabk%2B%2FxTp%2FLkpgxadaFhK25QrF%2FB%2BkjAPiI1ZXkEJS8sTBthDp7IZvLdeiNvLegY%2Fijrzc1QqhFfKVkdvcAXSmF79ew9Bh3QhOzhrD6PZy8DISX5QyM2kUNBWFxDVN8Ts25oIgBc2apN73RX%2FhY7EVbBT5Fg69KMJGMgdD2ZSBYyLqT9TL0dITUrhAgDVe895Dwh%2FK1KRrxi%2Fp312C5gWEKPBJsZpPkUVp54Bs2ko3MCMJJwNPWZYHY%2Bxp%2F4nv7qB%2FLWW0tVfI33ylpi8DtVTuvDzPKXRoWUmCRLLTnGPuGS5sWoNY5zRxlLtgM%2FHE4gq0fUmQ%3D%3D