Row Space: Linear Algebra, Matrix (Mathematics), Linear Combination, Euclidean Subspace, Euclidean Space - Tapa blanda

Row Space

Taschenbuch. Condición: Neu. This item is printed on demand - Print on Demand Titel. Neuware -Please note that the content of this book primarily consists of articlesavailable from Wikipedia or other free sources online. In linearalgebra, the row space of a matrix is the set of all possible linearcombinations of its row vectors. The row space of an m × n matrix is asubspace of n-dimensional Euclidean space. The dimension of the rowspace is called the rank of the matrix. Let A be an m × n matrix, withrow vectors r1, r2, ., rm. A linear combination of these vectors isany vector of the form c_1 textbf{r}_1 + c_2 textbf{r}_2 + cdots + c_mtextbf{r}_mtext{,} where c1, c2, ., cm are constants. The set of allpossible linear combinations of r1,.,rm is called the row space of A.That is, the row space of A is the span of the vectors r1,.,rm. Thedimension of the row space is called the rank of the matrix. This is thesame as the maximum number of linearly independent rows that can bechosen from the matrix. For example, the 3 × 3 matrix in the exampleabove has rank two. The rank of a matrix is also equal to the dimensionof the column space.VDM Verlag, Dudweiler Landstraße 99, 66123 Saarbrücken 76 pp. Englisch. Nº de ref. del artículo: 9786131259203

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