## Numerical Linear AlgebraA concise, insightful, and elegant introduction to the field of numerical linear algebra. Designed for use as a stand-alone textbook in a one-semester, graduate-level course in the topic, it has already been class-tested by MIT and Cornell graduate students from all fields of mathematics, engineering, and the physical sciences. The authors' clear, inviting style and evident love of the field, along with their eloquent presentation of the most fundamental ideas in numerical linear algebra, make it popular with teachers and students alike. |

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accuracy algorithm analysis applied approximation arithmetic Arnoldi backward becomes close column computed condition number consider convergence corresponding count deﬁned deﬁnite described determined diagonal dimension discussed eigenvalues eigenvectors entries equal errors example Exercise fact Figure ﬁrst ﬂoating point ﬂops follows formula function Gaussian elimination give given GMRES hermitian Householder idea introduced involving iteration known Lanczos least squares problem Lecture linear algebra mathematical matrix means methods minimal multiplication norm normal Note obtain operations orthogonal orthogonal matrix perturbations pivoting polynomial positive practice problem projector Proof QR algorithm QR factorization random rank reduced represented requires result Show singular values solution solve space stability standard step Suppose symmetric symmetric matrix Theorem triangular tridiagonal unitary values vector Write zeros