Antissümmeetrilised

Antissümmeetrilised refers to a property of certain mathematical objects, most commonly matrices, where negating the order of elements results in a sign change. In the context of matrices, a matrix A is considered antissymmetric if its transpose, denoted as A^T, is equal to its negative, i.e., A^T = -A. This means that for any element A_{ij} at row i and column j, the corresponding element A_{ji} at row j and column i will be the negative of A_{ij}, so A_{ji} = -A_{ij}.

A direct consequence of this definition is that all elements on the main diagonal of an antissymmetric matrix must be zero. This is because for a diagonal element A_{ii}, the condition A_{ii} = -A_{ii} can only be satisfied if A_{ii} = 0. Antissymmetric matrices have several important properties in linear algebra and other fields. For example, the determinant of an antissymmetric matrix of odd dimension is always zero. Antissymmetric matrices are closely related to skew-symmetric matrices, and the terms are often used interchangeably. They appear in various areas, including differential geometry, physics, and computer graphics, often when dealing with operations that change sign under reversal or transformation.

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