Linear algebra

Important notes:

• basis and change of basis
• singular value decomposition and polar decomposition
• symmetric matrix
• Jordan canonical form of a matrix
• projections
• matrix diagonalization
• bilinear forms diagonalization
• block matrix determinant formula
• n-volume in an m-dimensional vector space
• Hermitian form, inner product and symplectic form relationship
• determinant
• trace
• common eigenvectors