# MatrixAlg1.pdf - MATRICES (slightly modified content from...

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MATRICES(slightly modified content from Wikipedia articles on matrices(mathematics))Amatrixis a rectangular array ofnumbersor other mathematical objects, for which operations such asadditionandmultiplicationare defined. Mostof this article focuses onrealmatrices, i.e., matrices whose elements arereal numbers. For instance, this is a real matrix:The numbers, symbols or expressions in the matrix are called itsentriesor itselements. The horizontal and vertical lines of entries in a matrix arecalledrowsandcolumns, respectively. The size of a matrix is defined by the number of rows and columns that it contains. A matrix withmrows andncolumns is called anm×nmatrix orm-by-nmatrix, whilemandnare called itsdimensions. For example, the matrixAabove is a 3 × 2 matrix.Matrices which have a single row are calledrow vectors, and those which have a single column are calledcolumn vectors. A matrix which has thesame number of rows and columns is called asquare matrix.NameSizeExampleDescriptionRow vector1 ×nA matrix with one row, sometimes used to represent a vectorColumn vectorn× 1A matrix with one column, sometimes used to represent a vectorSquare matrixn×nA matrix with the same number of rows and columns.1. NotationMatrices are commonly written in box brackets:
The specifics of symbolic matrix notation varies widely, with some prevailing trends. Matrices are usually symbolized usingupper-caseletters (suchasAin the examples above), while the correspondinglower-caseletters, with two subscript indices (e.g.,a11, ora1,1), represent the entries.The entry in thei-th row andj-th column of a matrixAis sometimes referred to as thei,j, (i,j), or (i,j)thentry of the matrix, and most commonlydenoted asai,j, oraij. Alternative notations for that entry areA[i,j] orAi,j. For example, the (1,3) entry of the following matrixA

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