**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 |

**MA8251 Notes Engineering Mathematics 2 Unit 1** **Click here to Download**

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