| An Introductory Geometrical Application |
| Nested triangles / 1.1： |
| The transformation $\sigma$ / 1.2： |
| The transformation $\sigma$ iterated with different values of $s$ / 1.3： |
| Nested polygons / 1.4： |
| Introductory Matrix Material |
| Block operations / 2.1： |
| Direct sums / 2.2： |
| Kronecker product / 2.3： |
| Permutation matrices / 2.4： |
| The Fourier matrix / 2.5： |
| Hadamard matrices / 2.6： |
| Trace / 2.7： |
| Generalized inverse / 2.8： |
| Normal matrices, quadratic forms, and field of values / 2.9： |
| Circulant Matrices |
| Introductory properties / 3.1： |
| Diagonalization of circulants / 3.2： |
| Multiplication and inversion of circulants / 3.3： |
| Additional properties of circulants / 3.4： |
| Circulant transforms / 3.5： |
| Convergence questions / 3.6： |
| Some Geometric Applications of Circulants |
| Circulant quadratic forms arising in geometry / 4.1： |
| The isoperimetric inequality for isosceles polygons / 4.2： |
| Quadratic forms under side conditions / 4.3： |
| Nested n-gons / 4.4： |
| Smoothing and variation reduction / 4.5： |
| Applications to elementary plane geometry: n-gons and $K_r$-grams / 4.6： |
| The special case: $\text{circ}(s, t, 0, 0, \dots, 0)$ / 4.7： |
| Elementary geometry and the Moore-Penrose inverse / 4.8： |
| Generalizations of Circulants: $g$-Circulants and Block Circulants |
| $g$-circulants / 5.1： |
| $0$-circulants / 5.2： |
| PD-matrices / 5.3： |
| An equivalence relation on $\{1, 2, \dots, n\}$ / 5.4： |
| Jordanization of $g$-circulants / 5.5： |
| Block circulants / 5.6： |
| Matrices with circulant blocks / 5.7： |
| Block circulants with circulant blocks / 5.8： |
| Further generalizations / 5.9： |
| Centralizers and Circulants |
| The leitmotiv / 6.1： |
| Systems of linear matrix equations / 6.2： |
| The centralizer |
| $\div$ algebras / 6.3： |
| Some classes $Z(P_{\sigma}, P_{\tau})$ / 6.4： |
| Circulants and their generalizations / 6.5： |
| The centralizer of $J$; magic squares / 6.6： |
| Kronecker products of $I, \pi$, and $J$ / 6.7： |
| Best approximation by elements of centralizers / 6.8： |
| Appendix |
| Bibliography |
| Index of authors |
| Index of subjects |
| An Introductory Geometrical Application |
| Nested triangles / 1.1： |
| The transformation $\sigma$ / 1.2： |
図書
