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Lecture 31

MATH 417 Lecture 31: Day 31
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Department
Mathematics
Course
MATH 417
Professor
All Professors
Semester
Spring

Description
Chapter 7.1 Norm of Vectors Matrices RT is the set of n-dimensional column vectors w/ entries n R peh A vector norm on Rh is a junction n.ll from t Most impatant exampes fr us CEuclidarn Nom norm circle norm 30ware Ex Cauchy Schwara Tnegralty Het X, Y Chven. X Y Ex-yl is the distance bhu x t Y A Sempenoe to xe RR in the norm. if for every E o there is NOE) >O vice versa. Matrix Norms A mainx norm on the set of n x n matrices is a real-valued fanchon st. fr any e R and any nxn matrices A E B All The distance bhun A B 13 A B Chapter 7.1 Norm of Vectors Matrices RT is the set of n-dimensional column vectors w/ entries n R peh A vector norm on Rh is a junction n.ll from t Most impatant exampes fr us CEuclidarn Nom norm circle norm 30ware Ex Cauchy Schwara Tnegralty Het X, Y Chven. X Y Ex-yl is the distance bhu x t Y A Sempenoe to xe RR in the norm. if for every E o there is NOE) >O vice versa. Matrix Norms A mainx norm on the set of n x n matrices is a real-valued fanchon st. fr any e R and any nxn matrices A E B All The distance bhun A B 13 A BNatural Induced norms If M. is a nam on RR, the induced norm an the nxn matrices is An induced norm measures the maximum amout by which A stretches vados n R" wrt max stretch in ut x In. Then Ax EDT] max max row su
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