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Reinforce the fire mouth by stacking a column of bricks to the inside of each side wall.
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For a matrix A, the operate vec (A) is used for vectorizing A by stacking the columns of A into a column vector.
off(A) vanishes the diagonal components of the input matrix A. vec(A) reshapes a matrix A into a column vector by stacking its columns vertically.
A straightforward dimensionality reduction approach on input matrix data by means of orthogonal transformations can be carried out by stacking matrix columns into a single vector, as follows: χ ( k ) = ( x c 1 ( k ) ) ⊤, ( x c 2 ( k ) ) ⊤, …, ( x cT ( k ) ) ⊤ χ ( k ) ∈ R 1 × FT (1).
The vector operator creates a vector from a matrix by stacking the columns of the matrix on top of each other.
The operator bdiag forms a block diagonal matrix from its matrix arguments, while the operator vec transforms a matrix into a column vector by stacking the columns of its matrix argument one on top of the other one.
The operator vecdiag forms a column vector out of the main diagonal of its matrix argument, while 1 R denotes the "all-ones" vector of dimension R. The operator vec forms a vector by stacking the columns of its matrix argument.
E denotes the statistical expectation operator, vec denotes the vectorized form of a matrix which is obtained by stacking the columns of the matrix to form a long vector, and bdiag denotes block diagonal matrix.
Finally, the feature vector z(k) is obtained by stacking the columns of z k)into a new single feature vector.
The vec (A) denotes the column vector obtained by stacking the columns of A. The letter j represents the imaginary unit (i.e., (j=sqrt {-1})).
Then, we define the vector of coefficients (mathbf {w}(k) = text {vec}left (mathbf {W} k)right)) to be the vectorization of W k)—i.e. (mathbf {w}(k) in mathbb {C}^{N(L+1)} ) is formed by stacking the columns of the matrix W(k) into a single column vector.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com