Matrix Inversion And the Solution of Linear Equations
Matrix Inversion And the Solution of Linear Equations
J H Curtiss
The book Matrix Inversion And the Solution of Linear Equations was written by author J H Curtiss Here you can read free online of Matrix Inversion And the Solution of Linear Equations book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is Matrix Inversion And the Solution of Linear Equations a good or bad book?
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2) is to prove that b. = j "b'' ^ j, at the same time showing that | b "^ j :; ^i^i * ^'® have |a"l!.^M = ^ b'^""^ k?! ^^ k^i a ik /t b. R.^a^^/ « Ostrowski (1952) 1-41 "'e leave the remainder of the proof of (1. 4. 2) to the reader. A3 for (1. 4. 3), we have a b -1 .^V^ %h^^1^ h I r* Ik The reader should have no difficulty in proceedins; from here. ) '''} 10. Let A = a '^ be a complex n x n matrix and letos be a L -I -^ g \ complex n X 1 matrix with elements y"^, y'^, •••^ y^ • Further, let A ...and*Y^have the following property; ii > y ij , i = 1, , n, where r is some positive num. Ber. Prove that the system of linear equations represented by A € -^ has a unique solution /J IP T-l 111 C =(x, x, ... , x) such that Ix | ^ r, 1 - 1, ... , n. (Hint: Of course the existence and uniqueness of the solution I kl I 1 1 21 is assured by Exercise B. Let |x ! be the maximum of x, ^ ]' ... , |x"|, and suppose that |x^|= r, in contradiction to the con- clusion stated above. Consider the eqiiation -a x r -y *^^ x .
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