Row and Column Spaces: Matrix (Math), Euclidean Subspace, Hamel Dimension, Rank (Linear Algebra), Linear Transformation - Brossura

 
9786131258459: Row and Column Spaces: Matrix (Math), Euclidean Subspace, Hamel Dimension, Rank (Linear Algebra), Linear Transformation

Sinossi

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The row and column space of an m-by-n matrix with real entries is the subspace of Rn generated by the row vectors and column vectors, respectiviely, of the matrix. Its dimension is equal to the rank of the matrix and is at most min(m,n). Intuitively, given a matrix A, the action of the matrix A on a vector x will return a linear combination of the columns of A weighted by the coordinates of x as coefficients. Another way to look at this is that it will (1) first project x into the row space of A, (2) perform an invertible transformation, and (3) place the resulting vector y in the column space of A. Thus the result y =A x must reside in the column space of A. See the singular value decomposition for more details on this second interpretation.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Altre edizioni note dello stesso titolo

9786132979155: Row and Column Spaces: Row Space, Column Space, Matrix (Math), Euclidean Subspace, Linear Transformation

Edizione in evidenza

ISBN 10:  6132979158 ISBN 13:  9786132979155
Casa editrice: OmniScriptum, 2026
Brossura