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# 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
• 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)

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 Subject name ENGINEERING MATHEMATICS 2 Regulation 2017 Regulation