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REDUCE THE QUADRATIC FROM TO CANONICAL FORM - Coggle Diagram
REDUCE THE QUADRATIC FROM TO CANONICAL FORM
QUADRANT FORM
General form
Matrix representation
Formula:1 .Quadratic Form
Q = X^TAX
SYMMETRIC MATRIX
Formation of matrix
SYMMETRIC condition
Formula:2. Symmetric Matrix
A = A^T
CHARACTERISTIC EQUATIONS
Determinant
Characteristics polynomial
Formula:3.Characteristic Equation
|A-\\lambda I|
EIGEN VALUES
Find the rools
Calculate eigenvalues
FORMULA: 4. Eigenvalues
\lambda_1,\lambda_2,\lambda_3
EIGEN VECTORS f
Solve equations
Formula:5. Eigenvectors
(A-\lambda I)X=0
Find corresponding vectors
ORTHOGONAL TRANSFORMATION
Transformation:X=PY
Normalize eigen vectors
Formula:6.Orthogonal Transformation
P^TP=IX=PY.