ENGG. MATRICES LEC 2 | FUNDAMENTALS OF ENGINEERING MATHS | ALL BRANCHES | DINESH SIR
DINESH SIR Live Study・2 minutes read
Matrices can be expressed as a sum of symmetric and skew symmetric parts by using specific formulas and calculations. The process involves finding the symmetric matrix (p) and the skew symmetric matrix (q), with practical examples provided to illustrate the concept and properties of these matrices.
Insights
- Any square matrix can be broken down into a sum of symmetric and skew symmetric matrices, showcasing the versatility and compositional nature of matrices in linear algebra.
- The process of converting matrices into Hermitian and skew Hermitian forms involves specific formulas and calculations, demonstrating a structured approach to transforming matrices and understanding their unique properties in complex analysis.
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Recent questions
What are symmetric and skew symmetric matrices?
Symmetric matrices have elements mirrored across the main diagonal, while skew symmetric matrices have elements that are negatives of each other across the main diagonal.
How can a square matrix be expressed as symmetric and skew symmetric matrices?
Any square matrix can be expressed as the sum of a symmetric matrix and a skew symmetric matrix.
What is the formula to calculate a symmetric matrix?
The formula to calculate a symmetric matrix is 1/2(a + a transpose), where 'a' is the original matrix.
How do you find the skew symmetric matrix of a square matrix?
The skew symmetric matrix can be found using the formula 1/2(a - a transpose), where 'a' is the original matrix.
What are the properties of Hermitian and skew Hermitian matrices?
Hermitian matrices have elements that are equal to their complex conjugates, while skew Hermitian matrices have elements that are negatives of their complex conjugates.
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