ulab.linalg – Linear algebra functions¶
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ulab.linalg.cholesky(A: ulab.array) → ulab.array¶ - Parameters
A (array) – a positive definite, symmetric square matrix
- Return ~ulab.array L
a square root matrix in the lower triangular form
- Raises
ValueError – If the input does not fulfill the necessary conditions
The returned matrix satisfies the equation m=LL*
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ulab.linalg.det(m: ulab.array) → float¶ - Param
m, a square matrix
- Return float
The determinant of the matrix
Computes the eigenvalues and eigenvectors of a square matrix
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ulab.linalg.dot(m1: ulab.array, m2: ulab.array) → Union[ulab.array, float]¶ -
Computes the product of two matrices, or two vectors. In the letter case, the inner product is returned.
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ulab.linalg.eig(m: ulab.array) → Tuple[ulab.array, ulab.array]¶ - Parameters
m – a square matrix
- Return tuple (eigenvectors, eigenvalues)
Computes the eigenvalues and eigenvectors of a square matrix
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ulab.linalg.inv(m: ulab.array) → ulab.array¶ - Parameters
m (array) – a square matrix
- Returns
The inverse of the matrix, if it exists
- Raises
ValueError – if the matrix is not invertible
Computes the inverse of a square matrix
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ulab.linalg.norm(x: ulab.array) → float¶ - Parameters
x (array) – a vector or a matrix
Computes the 2-norm of a vector or a matrix, i.e.,
sqrt(sum(x*x)), however, without the RAM overhead.
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ulab.linalg.trace(m: ulab.array) → float¶ - Parameters
m – a square matrix
Compute the trace of the matrix, the sum of its diagonal elements.