Page 257 - Linear Algebra Done Right

Index

absolute value, 69 complex number, 2
addition, 9 complex spectral theorem,
adjoint, 118 133
complex vector space, 10
basis, 27 conjugate transpose, 120
block diagonal matrix, 142 coordinate, 4
block upper-triangular matrix, cube, 238
195 cube root of an operator,
159
Cauchy-Schwarz inequality,
104
Cayley-Hamilton theorem for degree, 22
complex vector derivative, 241
spaces, 173 determinant of a matrix,
229
Cayley-Hamilton theorem for
determinant of an operator,
real vector spaces,
207 222
change of basis, 216 diagonal matrix, 87
characteristic polynomial of a diagonal of a matrix, 83
2-by-2 matrix, 199 differentiable, 241
dimension, 31
characteristic polynomial of an
operator on a complex direct sum, 15
vector space, 172 divide, 180
characteristic polynomial of an division algorithm, 66
operator on a real dot product, 98
vector space, 206
characteristic value, 77 eigenpair, 205
closed under addition, 13 eigenvalue of a matrix, 194
closed under scalar eigenvalue of an operator,
multiplication, 13 77
complex conjugate, 69 eigenvector, 77

249