User:IssaRice/Linear algebra/

Index of pages in this directory:

• IssaRice/Linear algebra/
• A matrix is only similar to itself if and only if it is a scalar multiple of the identity matrix
• Change of basis example in two dimensions
• Classification of operators
• Deriving projection formula and equivalent formulas for dot product
• Determinant as signed volume of transformation
• Determinant of matrix equals product of eigenvalues
• Dual basis
• Dual space of vector space of polynomials
• Equivalent statements for injectivity and surjectivity
• Geometry of linear transformations
• How to remember the projection formula
• Invertible equals expressible as change of coordinate matrix
• Linear transformation vs matrix views
• List of matrix products
• Matrix of a linear transformation
• Outline of linear algebra
• Properties of a list of vectors and their images
• Properties preserved under various operations to a matrix
• Rank
• Rank of polynomial matrix is constant everywhere except possibly at finitely many points
• Riesz representation theorem
• Singular value decomposition
• Trace of matrix equals sum of eigenvalues
• Type checking vector spaces