BE(ECE) & ME Communication systems. Passion to teach. Enjoy making crafts. "By learning u teach, by teaching u learn".   

Sugantha Haridass

With the help of this course we Get to know about characteristic equation, eigenvalues values and eigen vectors

English

Matrices - Engineering Mathematics - II

This is a part of Unit 1 in Engineering Mathematics-2, About the Characteristic equation, Eigenvalues and Eigenvectors. The 3 steps involved are clearly explained with example.

Characteristic Equation, Eigenvalues and Eigenvectors

Quick look on Synthetic Division, Cross multiplication and Determinant of a matrix which play important role in the formation of Eigen Vectors.

Determinant, Synthetic Division and Cross Multiplication

Formation of eigenvectors with non-repeated and repeated eigenvalues .

Eigen Vectors for Repeated and Non-Repeated Eigenvalues

8 important properties of Eigenvalues. Sum and product of eigenvalues, eigen value of inverse matrix, matrix transpose, triangular matrix, positive power matrix and so.

Properties of Eigenvalues

Statement of Cayley Hamilton Theorem with example. Finding positive powers of a matrix and inverse of matrix using the theorem

Cayley Hamilton Theorem

Transformation of a Symmetric Matrix to Diagonal matrix.The values in the main diagonal of the diagonal matrix should be the eigen values of the given Symmetric Matrix.  It involves 7 steps.

Orthogonal Transformation Of A Symmetric Matrix To Diagonal Form

Quadratic form and its nature based on eigen values.

Quadratic Form

Quadratic form has all terms with degree 2. Canonical form has all terms as square terms. Here is the explanation for Orthogonal reduction of quadratic form to Canonical Form which involves 8 steps.

Lessons

8 lessons • 1h 27m

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Characteristic Equation, Eigenvalues and Eigenvectors

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Determinant, Synthetic Division and Cross Multiplication

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Eigen Vectors for Repeated and Non-Repeated Eigenvalues

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Properties of Eigenvalues

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Cayley Hamilton Theorem

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Orthogonal Transformation Of A Symmetric Matrix To Diagonal Form

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Quadratic Form

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Orthogonal Reduction Of Quadratic Form To Canonical Form