Student[NumericalAnalysis][IsMatrixShape] - Check whether a matrix is a certain shape or not
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Calling Sequence
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IsMatrixShape(A, shape)
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Parameters
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A
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Matrix
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shape
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name; must be one of diagonal, strictlydiagonallydominant, diagonallydominant, hermitian, positivedefinite, symmetric, triangular[upper], triangular[lower], or tridiagonal
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Description
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The IsMatrixShape command verifies whether the matrix A is a certain "shape".
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The only types of "shapes" that the IsMatrixShape command can verify are:
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Diagonal : shape = diagonal
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Strictly diagonally dominant : shape = strictlydiagonallydominant
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Diagonally dominant : shape = diagonallydominant
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Hermitian : shape = hermitian
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Positive definite : shape = positivedefinite
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Symmetric : shape = symmetric
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Upper or lower triangular : shape = triangular[upper] or shape = triangular[lower], repectively
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Tridiagonal : shape = tridiagonal
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Notes
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If neither upper nor lower is specified, the triangular option defaults to triangular[upper].
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A complex n-by-n matrix A is positive definite if and only if A is Hermitian and for all n-dimensional complex vectors v, we have , where denotes the real part of a complex number.
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A real n-by-n matrix A is positive definite if and only if A is symmetric and for all n-dimensional real vectors v, we have .
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To check another "shape" that is not available with the Student[NumericalAnalysis][IsMatrixShape] command see the general IsMatrixShape command.
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Examples
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