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Lecture 30

MATH 417 Lecture 30: Day 30
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Department
Mathematics
Course
MATH 417
Professor
All Professors
Semester
Spring

Description
voting actorizatiar Lil If we can do Gaussian Elm an Anon woud pivoting, then A Lu LE laver trangle. angle. fer mutation matrices P has one na aero entry of l in each raw For any nasingular system Ax-b, there is a permutation matrix P st. PAX Pb can be solved for x wat now interchanges Ex3 pg. 408 Section 6.6 Matrices 3 3bructure of Matrices YDes Diagonally Dominant 2 9mmetric positive definite 3) Banded matrices Defn An nin, trix A is diagonally doniront if mac Str diagonally daminat if Ge) is a strict ineguality Tkm A strictly ding. dam. ix A is nonsingular, and we enn solve the system Ax b ul G-Elm uyat raw interchange This process is stable wrt growth of roundoff emors Elinurales piding. Res not reduce 4 geratas -Rehm A matrix A is positive de Ante Caymmetric posihve dehnute) if A is symmetric and XTAX o, v nonzero n- vectors x xTA w/ lo being the smallest eigenwalue of A The matrix is not SPD i rt has any negative eigenvalue Theorem If A is an SPD matrix, then A has an inverse ii) a ii >o voting actorizatiar Lil If we can do Gaussian Elm an Anon woud pivoting, then A Lu LE laver trangle. angle. fer mutation matrices P has one na aero entry of l in each raw For any nasingular system Ax-b, there is a permutation matrix P st. PAX Pb can be solved for x wat now interchanges Ex3 pg. 408 Section 6.6 Matrices 3 3bructure of Matrices YDes Diagonally Dominant 2 9mmetric positive definite 3) Banded matrices Defn An nin, trix A is diagonally doniront if mac Str diagonally daminat if Ge) is a strict ineguality Tkm A strictly ding. dam. ix A is nonsingular, and we e
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