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1

When powers of a matrix coincide with its Hadamard powers

100%

Drnovšek R.

Special Matrices

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2015

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tom 3

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nr 1

EN

We characterize matrices whose powers coincide with their Hadamard powers.

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Consimilarity and quaternion matrix equations AX −^X B = C, X − A^X B = C

61%

Klimchuk T., Sergeichuk V. V.

Special Matrices

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2014

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tom 2

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nr 1

EN

L. Huang [Consimilarity of quaternion matrices and complex matrices, Linear Algebra Appl. 331 (2001) 21–30] gave a canonical form of a quaternion matrix with respect to consimilarity transformations A ↦ ˜S−1AS in which S is a nonsingular quaternion matrix and h = a + bi + cj + dk ↦ ˜h := a − bi + cj − dk (a, b, c, d ∈ ℝ). We give an analogous canonical form of a quaternion matrix with respect to consimilarity transformations A ↦^S−1AS in which h ↦ ^h is an arbitrary involutive automorphism of the skew field of quaternions. We apply the obtained canonical form to the quaternion matrix equations AX −^X B = C and X − A^X B = C.

3

New iterative codes for𝓗-tensors and an application

61%

Wang F., Sun D.

Open Mathematics

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2016

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tom 14

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nr 1

212-220

EN

New iterative codes for identifying 𝓗 -tensor are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor, i.e., an even-degree homogeneous polynomial form are given. Advantages of results obtained are illustrated by numerical examples.

Ograniczanie wyników

2 Special Matrices

1 Open Mathematics

1 Drnovšek R.

1 Klimchuk T.

1 Sergeichuk V. V.

1 Sun D.

1 Wang F.

1 2016

1 2015

1 2014

When powers of a matrix coincide with its Hadamard powers

Consimilarity and quaternion matrix equations AX −^X B = C, X − A^X B = C

New iterative codes for𝓗-tensors and an application