Contents

Exercises

Exercises 1-7

-Hungarian method
-Matrix addition and multiplication
-Transpose
-Symmetricity
-Commutation
-Coefficient matrix for a linear system of equations

Exercises 8-10

-Inverse matrix
-Conjugate matrix

Exercises 11-15

-Orthogonality
-Gaussian elimination

Exercises 16-22

-Computation of an inverse matrix
-LU decomposition
-QR decomposition

Exercises 23-31

-Basis
-Linear mapping
-Rank
-Nullity
-Kernel
-Basis for a kernel
-Determinant

Exercises 32-35

-Determinant
-Eigenvalues- and vectors

Exercises 36-44

-Diagonalization
-Linear system of differential equations

Exercises 45-54

-Linear system of differential equations
-Gershgorin discs
-Numerical computation of eigenvalues
-Matrix norms
-Condition number
-Spectral radius

Exercises 55-60

-Jacobi method
-Gauss-Seidel method
-Least squares method
-Pseudo inverse
-Characteristic polynomial
-Cayley-Hamilton theorem

Exercises 61-64

-Applications of the Cayley-Hamilton theorem


Index
Contents