MA8251 Notes Engineering Mathematics 2 Unit 1
MA8251 Notes Engineering Mathematics 2 Unit 1 Matrix Regulation 2017 For Anna University Free download. ENGINEERING MATHEMATICS 2 MA8251 Unit 1 Notes Pdf Free download.
Content MA8251 Notes Engineering Mathematics 2 Unit 1 Matrix:
- MATRIX
- CHARACTERISTIC EQUATION
- EIGEN VALUE
- EIGEN VECTOR
- LINEARLY DEPENDENT AND INDEPENDENT EIGEN VECTOR
- PROPERTIES OF EIGEN VALUES AND EIGEN VECTORS:
- CAYLEY HAMILTON THEOREM:
- DIAGONALISATION OF A MATRIX
- DIAGONALISATION BY ORTHOGONAL
- TRANSFORMATION OR ORTHOGONAL REDUCTION
- QUADRATIC FORMS
- NATURE OF QUADRATIC FORMS:
- RULES FOR FINDING NATURE OF QUADRATIC FORM USING PRINCIPAL SUBDETERMINANTS (ma8251 notes engineering mathematics 2 unit 1)
CHARACTERISTIC EQUATION Let ‘A’ be a given matrix. Let λ be a scalar. The equation det [A- λ I]=0 is called the characteristic equation of the matrix A.
EIGEN VALUE The values of λ obtained from the characteristic equation |A- λ I|=0 are called the Eigen values of A.
EIGEN VECTOR Let A be a square matrix of order ‘n’ and λ be a scalar, X be a non- zero column vector such that AX = λX. (ma8251 notes engineering mathematics 2 unit 1)
LINEARLY DEPENDENT AND INDEPENDENT EIGEN VECTOR Let ‘A’ be the matrix whose columns are eigen vectors. (i) If |A|=0 then the eigen vectors are linearly dependent. (ii) If |A|=!0 then the eigen vectors are linearly independent.
PROPERTIES OF EIGEN VALUES AND EIGEN VECTORS:
Property 1: (I) The sum of the Eigen values of a matrix is equal to the sum of the elements of the principal diagonal (trace of the matrix). i.e., λ1+ λ2+ λ3=a11+a22+a33 (ii)The product of the Eigen values of a matrix is equal to the determinant of the matrix. i.e., λ1 λ2 λ3=|A|
Property 2: A square matrix A and its transpose ܣ have the same Eigen values.
Property 3: The characteristic roots of a triangular matrix are just the diagonal elements of the matrix.
Property 4: If λ is an Eigen value of a matrix A, then 1/ λ, (λ=!0) is the Eigen value of A-1
Property 5: If λ is an Eigen value of an orthogonal matrix A, then 1/ λ, (λ=!0) is also its Eigen value. (ma8251 notes engineering mathematics 2 unit 1)
| Subject name | ENGINEERING MATHEMATICS 2 |
| Regulation | 2017 Regulation |
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