Adjoint of a linear operator 355

Adjoint of a matrix 329

Bilinear form 419

Complex inner product space 330

Condition number 463

Congruent matrices 423

Conjugate transpose (adjoint) of a matrix 329

Critical point 436

Diagonalizable bilinear form 425

Fourier coefficients of a vector relative to an orthonormal set 345

Frobenius inner product 330

Gram-Schmidt orthogonalization process 342

Hessian matrix 436

Index of a bilinear form 441

Index of a matrix 442

Inner product 327

Inner product space 330

Invariants of a bilinear form 441

Invariants of a matrix 442

Least squares line 358

Legendre polynomials 344

Local extremum 436

Local maximum 436

Local minimum 436

Matrix representation of a bilinear form 421

Minimal solution of a system of equations 361

Norm of a matrix 461

Norm of a vector 331

Normal matrix 367

Normal operator 367

Normalizing a vector 333

Orthogonal complement of a subset of an inner product space 347

Orthogonally equivalent matrices 381

Orthogonal matrix 379

Orthogonal operator 376

Orthogonal projection 395

Orthogonal projection on a subspace 348

Orthogonal subset of an inner product space 333

Orthogonal vectors 333

Orthonormal basis 339

Orthonormal set 333

Penrose conditions 418

Polar decomposition of a matrix 409

Pseudoinverse of a linear transformation 410

Pseudoinverse of a matrix 411

Quadratic form 430

Rank of a bilinear form 439

Rayleigh quotient 461

Real inner product space 330

Reflection 467

Resolution of the identity operator induced by a linear transformation 399

Rigid motion 383

Rotation 467

Self-adjoint matrix 370

Self-adjoint operator 370

Signature of a form 441

Signature of a matrix 442

Singular value decomposition of a matrix 407

Singular value of a linear transformation 404

Singular value of a matrix 406

Space-time coordinates 449

Spectral decomposition of a linear operator 399

Spectrum of a linear operator 399

Standard inner product 328

Symmetric bilinear form 425

Translation 383

Trigonometric polynomial 396

Unitarily equivalent matrices 381

Unitary matrix 379

Unitary operator 376

Unit vector 333