linear algebra, an augmented matrix ( A | B ) {\displaystyle (A\vert B)} is a k × ( n + 1 ) {\displaystyle k\times (n+1)} matrix obtained by appending...

Using an augmented matrix and an augmented vector, it is possible to represent both the translation and the linear map using a single matrix multiplication...

matrices. With respect to an n-dimensional matrix, an n+1-dimensional matrix can be described as an augmented matrix. In the physical sciences, an active transformation...

invertible matrix (non-singular, non-degenarate or regular) is a square matrix that has an inverse. In other words, if some other matrix is multiplied...

find the inverse of this matrix, one takes the following matrix augmented by the identity and row-reduces it as a 3 × 6 matrix: [ A | I ] = [ 2 − 1 0 1...

meaning it has no solutions, if the rank of the augmented matrix (the coefficient matrix augmented with an additional column consisting of the vector...

otherwise) is inconsistent if the rank of the augmented matrix is greater than the rank of the coefficient matrix. If, on the other hand, the ranks of these...

lengthening or widening of rhythm or interval Augment (album), an album by Erra Augmented matrix, in mathematics, a matrix formed by placing two other matrices...

system is inconsistent if the rank of the augmented matrix is greater than the rank of the coefficient matrix. If on the other hand, the ranks of these...

of a system of linear equations, given the ranks of its augmented matrix and coefficient matrix. The theorem is variously known as the: Rouché–Capelli...

consistent if and only if the coefficient matrix has the same rank as its augmented matrix (the coefficient matrix with an extra column added, that column...

kernel of a matrix may be computed by Gaussian elimination. For this purpose, given an m × n matrix A, we construct first the row augmented matrix [ A I ]...

system of linear equations is said to be in row echelon form if its augmented matrix is in row echelon form. Similarly, a system of linear equations is...

The Matrix is a 1999 science fiction action film written and directed by the Wachowskis. It is the first installment in the Matrix film series, starring...

rectangular matrix A {\displaystyle A} , let A ~ = [ 0 A A ∗ 0 ] {\textstyle {\tilde {A}}={\begin{bmatrix}0&A\\A^{*}&0\end{bmatrix}}} be its augmented matrix. It...

transformations such that the 2×2 matrix of the A i , j {\displaystyle A_{i,j}} is orthogonal. The augmented matrix that represents the composition of...

it has more than one solution. This occurs when the matrix of the system and its augmented matrix have the same rank r and r < n. In this case, one can...

Then if and only if the rank of the augmented matrix [A | b] is also 2, there exists a solution of the matrix equation and thus an intersection point...

( p + n ) × ( p + n ) {\displaystyle (p+n)\times (p+n)} Hermitian augmented matrix [ 0 M M ∗ 0 ] . {\displaystyle {\begin{bmatrix}0&M\\M^{*}&0\end{bmatrix}}...

if the rank of the coefficient matrix is equal to the rank of the augmented matrix (the coefficient matrix augmented with a column of intercept terms)...

Gaussian-elimination consists of performing elementary row operations on the augmented matrix [ M v ] = [ 2 1 − 1 8 − 3 − 1 2 − 11 − 2 1 2 − 3 ] {\displaystyle \left[\...

{v1, ..., vk} are written as a matrix A {\displaystyle A} , then applying Gaussian elimination to the augmented matrix [ A A T | A ] {\displaystyle \left[AA^{\mathsf...

the objective, but the augmented Lagrangian method adds yet another term designed to mimic a Lagrange multiplier. The augmented Lagrangian is related to...

equations in a system equals the rank of the augmented matrix of the system—the system's coefficient matrix with one additional column appended, that column...

matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries...

F}\|[E\;F]\|_{F},\qquad (X+E)B=Y+F} where [ E F ] {\displaystyle [E\;F]} is the augmented matrix with E and F side by side and ‖ ⋅ ‖ F {\displaystyle \|\cdot \|_{F}}...

Numbers t1, t2, ..., tk such that v = t1b1 + ··· + tkbk Create an augmented matrix A whose columns are b1,...,bk , with the last column being v. Use elementary...

consistent if and only if its coefficient matrix has the same rank as does its augmented matrix (the coefficient matrix with an extra column added, that column...

1\}^{k}\to \{0,1\}^{2^{k}}} . The generator matrix of the augmented Hadamard code is obtained by restricting the matrix G {\displaystyle G} to the columns whose...

chromatic semitone. The augmented unison is abbreviated A1, or aug 1. Its inversion is the diminished octave (d8, or dim 8). The augmented unison is also the...