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Is a 'column vector' actually a vector or a matrix?
A vector is just an element of a vector space. A column vector is an element of the vector space of all column vectors. So in that sense, all column vectors are vectors. As for whether a given vector "is" a column vector, this is just a matter of convention and depends on the mood of the author.linear algebra - Column Vectors orthogonal implies Row Vectors also ...
Column vectors are orthogonal, but row vectors are not orthogonal. On the other hand, orthonormality of columns guarantees orthonormality of rows, and vice versa. As a footnote, one of the forms of Hadamard's inequality concerns the absolute value of the determinant of a matrix given the norms of the column vectors.What is the difference, geometrically, between row vectors and column ...
So is this different from having your space made of all row vectors with n components? Generally: what is the geometrical interpretation of the distinction between row vectors and column vectors? (As I understand it, algebraically, vectors are just ordered list of numbers.Row vector vs. Column vector - Mathematics Stack Exchange
Indeed, it's often just aesthetics; given a vector space of column vectors, it's isomorphic to the vector space of row vectors (the isomorphism being the transpose map). The distinction is nontrivial when you let matrices act upon vectors, however: the matrix must act from the left, with a column, and from the right, with rows.linear algebra - Why is the determinant zero iff the column vectors are ...
The determinant of a square matrix is zero if and only if the column vectors are linearly dependent. I see a lot of references to this all over the web, but I can't find an actual explanation for t...linear algebra - What exactly are the rows of a matrix and how come ...
Summary: In a nutshell, the columns represent the images of the standard basis vectors for the linear transformation, and the rows represent the images of the dual standard basis vectors for the dual transformation.Reason for thinking of vector as "row" and "column" vectors in linear ...
Supposing columns are used, the effect of a linear map on the coordinates of the vectors it operates on is given by left-multpication by the matrix of the linear map, and that operation requires the coordinates of the vector acted upon to be written as a column vector in the matrix product.mathematical difference between column vectors and row vectors
I'm writing a mathematical library; and I have an idea where I want to automatically turn column matrices and row matrices to vectors, with all of the mathematical properties of a vector.© 2008 - Mentions légales [ Modifiez votre fiche ] [ Inscrivez une fiche ]