Keyword Analysis & Research: basis for 3x3 symmetric matrix

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What is the smallest subspace of 3x3 matrices?

The trivial substace, consisting of a 3x3 null-matrix, is the smallest subspace of the vector space of all symmetric and lower-triangular 3x3 matrices, since it contains only one element, the 3x3 null-matrix, which satisfies both of your conditions.

Does a symmetric matrix be always square matrix?

A symmetric matrix will hence always be square . Some examples of symmetric matrices are: Addition and difference of two symmetric matrices results in symmetric matrix. If A and B are two symmetric matrices and they follow the commutative property, i.e. AB =BA, then the product of A and B is symmetric.

What is the eigen value of a real symmetric matrix?

Jacobi method finds the eigenvalues of a symmetric matrix by iteratively rotating its row and column vectors by a rotation matrix in such a way that all of the off-diagonal elements will eventually become zero , and the diagonal elements are the eigenvalues.

Do similar matrices have the same eigenvectors?

Similar matrices describe the same linear transformation with respect to different bases. Since eigenvalues and eigenvectors are determined by the transformation, you'll get the same ones if you use similar matrices.