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srinivasanlsn
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hi friends please help in finding out the ans for this . A 3x3 matrix was given , am asked to find algebraic multiplicity of it ! how to find algebraic multiplicity of 3x3 matrix ??
To find the determinant of a 4x4 matrix, you could use the basic definition- but that's very difficult. Most people use "expansion by minors".srinivasanlsn said:my next question is how to find determinant of 4x4 matrix ??
The algebraic multiplicity of a matrix is the number of times a specific eigenvalue appears as a root of the characteristic polynomial of the matrix.
The algebraic multiplicity is always greater than or equal to the geometric multiplicity of a matrix. Geometric multiplicity refers to the number of linearly independent eigenvectors corresponding to an eigenvalue, while algebraic multiplicity refers to the power of that eigenvalue in the characteristic polynomial.
No, the algebraic multiplicity of a matrix cannot be greater than its dimension. The algebraic multiplicity is always less than or equal to the dimension of the matrix.
The algebraic multiplicity can be determined by finding the eigenvalues of the matrix and then computing the power of each eigenvalue in the characteristic polynomial.
A zero algebraic multiplicity of a matrix signifies that the matrix has no real or complex eigenvalues. This means that the characteristic polynomial has no real or complex roots, and therefore the matrix is non-diagonalizable.