Sentence examples for matrix and left from inspiring English sources
where (mathbf {Q}_{R,i}in {mathbb {C}^{Ntimes {M}}}) for i=1,2 is a unitary matrix and (left {mathbf {R}_{1}, mathbf {R}_{2}right } in {mathbb {C}^{Mtimes {M}}}) are upper triangular matrices.
CT^{ Y } varepsilon^{Y} textT^{Y} Solving each equation for ( T^{Y} ) yields T^{Y} = left( {I - C} right)^{ - 1} varepsilon^{Y} T^{Y} text,,Ivarepsilon^{Y} + Cvarepsilon^{Y} + C^{2} varepsilon^{Y} + C^{3} varepsilon^{Y} + cdotextT^{e ( I ) denotes the m × m unit matrix and ( left( {I - C} right)^{ - 1} ) is Leontief inverse matrix.
Solving each equation for ( T^{ Y } yields T^{ Y } left( {I - C} right)^{ - 1} varepsilon^{Y} T^{Y} = Ivarepsileft{Y} + CvarepsIlon^{Y} + C^{2} varepsilon^{Y} + C^{3} varepsilon^{Y} + cdots where I denotes the m × m unit matrix and ( left( {I - C} right)^{ - 1} ) is Leontief invarepsilon^{.
(Had Mr. Godard confined his example to "The Matrix" and left Spielberg out of it, perhaps all this would be more clear).
Moreover, the silicone polishers may wear the resin matrix and left the filler particles protruding while it also scratches the resin surface [23], and produced a rougher surface in the silorane resin composite.
The Fn coating was done first and explants were placed on the matrix and left to attach for 30 min. Incubated beads were added in the dish and kept outside the Fn region.
This adaptation usually results in cardiac remodeling, which is characterized by severe structural changes of myocardial tissue, modification of the extracellular matrix, and reshaping of left ventricle geometry and performance.
Alternatively, one can apply the SVD decomposition to the original trajectory matrix M i in which case the outputs are two matrices containing the right and left singular vectors U and V and a diagonal matrix Σ containing the singular values.
We define diag n as an all-zero N×N matrix except the (left (N-left |nright |right times left (N-left |nright |right)) diagonal matrix in its top-right corner (n>0) or bottom-left corner (n<0), and diag0=diag.
We refer to (mathbf{G}= [ G_{alphabeta} ] inmathfrak {B} ( mathfrak{h} oplusmathfrak{h} ) ), as the coefficient matrix, and V as the left process generated by G.
The matrix Match (right, left) (resp., Match (left, right)) contains all possible matches between right and left primitives (resp., between left and right primitives).
