Abstract linear algebra - download pdf or read online

By Morton L. Curtis, Paul Place

ISBN-10: 0387972633

ISBN-13: 9780387972633

ISBN-10: 3540972633

ISBN-13: 9783540972631

Starting from scratch and constructing the traditional themes of Linear Algebra, this publication is meant as a textual content for a primary path at the topic. The objective to which this paintings leads is the concept of Hurwitz - that the one normed algebras over the true numbers are the true numbers, the advanced numbers, the quaternions, and the octonions. certain in proposing this fabric at an easy point, the publication stresses the total logical improvement of the topic and should supply a bavuable reference for mathematicians often.

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Z) = (- I. 2. 2). 'The row picture has th= planes from three equations. All the planes go through this solution. The original planes are sloping. t plane 4: = 8 after elimination is horizontal. "The column picture shows a combination of column ,'ectors producing the righl side h . y. Z multiply columns I. 2. 3 in the original system Ax "", b and also in the triangular system Ux '" c. fVr a 4 by 4 problem. or an n by n problem. >ds lhe same " ·a)". Here is the whole idea of forward elimination. column by column: Column 1.

So that a ;} is an enll)' in row i . The sewnd index j gi,'cs the col umn number. But those subscri pts are not convcnient on a keyboard! ln Slcad of oi) it is easier to type A(I . j). , O~J = A(5. 7) ""Quid 1M in ro ... 5, colum" 7. A. [all OIl]. 2) . r-or an nI by n matri~. lhe row index i goes from 110m. TIle column index j stops at n. ~. A squart: matrix (order,, ) 1Ias,,2 enlrics. Mulliplication in MATlAB I want to express A and x and their product Ax using MATlAB commands. This is a first step in learning that language.

Matrix addition is easy. The serious qucstion is mmnx mllu,'p/icolion. When can we multiply A times B. and what is the prodllCt AB? We canOOl multiply " 'hen A and B are 3 by 2. s. If A has LwO columns. B mu'\L ha>-e two rows. When A i~ 3 by 2. the matrix tJ un be 2 by I (a "«Lor) or 2 by 2 (square) or 2 by 20. E>-ery column of B is ready to be multiplied by A. Tkn A B i! 3 by I (a >-eclor) or 3 by 2 or 3 by 20.

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Abstract linear algebra by Morton L. Curtis, Paul Place

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