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A system of linear equations is said to be in row echelon form if its augmented matrix is in row echelon form. Similarly, a system of linear equations is said to be in reduced row echelon form or in canonical form if its augmented matrix is in reduced row echelon form. The canonical form may be viewed as an explicit solution of the linear system.
Anton, Howard (2005), Elementary Linear Algebra (Applications Version) (9th ed.), Wiley International Banerjee, Sudipto; Roy, Anindya (2014), Linear Algebra and Matrix Analysis for Statistics , Texts in Statistical Science (1st ed.), Chapman and Hall/CRC, ISBN 978-1420095388
Unlike abstract algebra, elementary algebra is not concerned with algebraic structures outside the realm of real and complex numbers. It is typically taught to secondary school students and at introductory college level in the United States, [5] and builds on their understanding of arithmetic. The use of variables to denote quantities allows ...
Lay, David C. (August 22, 2005), Linear Algebra and Its Applications (3rd ed.), Addison Wesley, ISBN 978-0-321-28713-7 Meyer, Carl D. (February 15, 2001), Matrix Analysis and Applied Linear Algebra , Society for Industrial and Applied Mathematics (SIAM), ISBN 978-0-89871-454-8 , archived from the original on March 1, 2001
Normally, a matrix represents a linear map, and the product of a matrix and a column vector represents the function application of the corresponding linear map to the vector whose coordinates form the column vector. The change-of-basis formula is a specific case of this general principle, although this is not immediately clear from its ...
Multilinear maps and multilinear forms are fundamental objects of study in multilinear algebra. If all variables belong to the same space, one can consider symmetric, antisymmetric and alternating k-linear maps. The latter two coincide if the underlying ring (or field) has a characteristic different from two, else the former two coincide.