Row- and column vectors

Summary

• A row vector is a matrix with only one row (dimension \(1×n\) ). If \(u\) is a row vector then the element at column \(j\) is denoted by \(u_j\) .
• A column vector is a matrix with only one column (dimension \(n×1\) ). If \(u\) is a column vector then the element at row \(i\) is denoted by \(u_i\) .
• A vector is an \(n\) -tuple (not a matrix). There is a one-to-one correspondence between a row vector and a vector and between a column vector and a vector.
• Notation: The entire row \(i\) of a matrix \(A\) is denoted by \(a_{i,:}\) or \(a_{i,⋅}\) . \(a_{i,:}\) is a row vector.
• Notation: The entire column \(j\) of a matrix \(A\) is denoted by \(a_{:,j}\) or \(a_{⋅,j}\) . \(a_{:,j}\) is a column vector.