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  2. Kernel (image processing) - Wikipedia

    en.wikipedia.org/wiki/Kernel_(image_processing)

    In image processing, a kernel, convolution matrix, or mask is a small matrix used for blurring, sharpening, embossing, edge detection, and more. This is accomplished by doing a convolution between the kernel and an image .

  3. Kernel (linear algebra) - Wikipedia

    en.wikipedia.org/wiki/Kernel_(linear_algebra)

    For this purpose, given an m × n matrix A, we construct first the row augmented matrix [], where I is the n × n identity matrix. Computing its column echelon form by Gaussian elimination (or any other suitable method), we get a matrix [ B C ] . {\displaystyle {\begin{bmatrix}B\\\hline C\end{bmatrix}}.}

  4. Kernel method - Wikipedia

    en.wikipedia.org/wiki/Kernel_method

    Kernel methods owe their name to the use of kernel functions, which enable them to operate in a high-dimensional, implicit feature space without ever computing the coordinates of the data in that space, but rather by simply computing the inner products between the images of all pairs of data in the feature space. This operation is often ...

  5. Matrix decomposition - Wikipedia

    en.wikipedia.org/wiki/Matrix_decomposition

    A ‘quasimatrix’ is, like a matrix, a rectangular scheme whose elements are indexed, but one discrete index is replaced by a continuous index. Likewise, a ‘cmatrix’, is continuous in both indices. As an example of a cmatrix, one can think of the kernel of an integral operator.

  6. Eigenvalue algorithm - Wikipedia

    en.wikipedia.org/wiki/Eigenvalue_algorithm

    Given an n × n square matrix A of real or complex numbers, an eigenvalue λ and its associated generalized eigenvector v are a pair obeying the relation [1] =,where v is a nonzero n × 1 column vector, I is the n × n identity matrix, k is a positive integer, and both λ and v are allowed to be complex even when A is real.l When k = 1, the vector is called simply an eigenvector, and the pair ...

  7. Identity matrix - Wikipedia

    en.wikipedia.org/wiki/Identity_matrix

    The th column of an identity matrix is the unit vector, a vector whose th entry is 1 and 0 elsewhere. The determinant of the identity matrix is 1, and its trace is . The identity matrix is the only idempotent matrix with non-zero determinant. That is, it is the only matrix such that:

  8. Gram matrix - Wikipedia

    en.wikipedia.org/wiki/Gram_matrix

    In the finite element method, the Gram matrix arises from approximating a function from a finite dimensional space; the Gram matrix entries are then the inner products of the basis functions of the finite dimensional subspace. In machine learning, kernel functions are often represented as Gram matrices. [2] (Also see kernel PCA)

  9. Gell-Mann matrices - Wikipedia

    en.wikipedia.org/wiki/Gell-Mann_matrices

    Since the eight matrices and the identity are a complete trace-orthogonal set spanning all 3×3 matrices, it is straightforward to find two Fierz completeness relations, (Li & Cheng, 4.134), analogous to that satisfied by the Pauli matrices. Namely, using the dot to sum over the eight matrices and using Greek indices for their row/column ...