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Matric Polynomial

An expression of the form

Let

The determinant

The equation

is called the characteristic equation of

The roots of the characteristic equation

**G(x) = A**_{0}x^{m}+ A_{1}x^{m-1}+ …. + A_{m-2}x^{2}+ A_{m-1}x + A_{m}, where**A**_{0}, A_{1}, …. , A_{m-1}, A_{m}are all square matrices of the same order, is said to be a matric polynomial of degree**m**if**A**. The coefficient of the highest power of_{0}≠ 0**x**, viz.**A**_{0}is called the leading coefficient. The matric polynomial is said to be**n**rowed if**n**is the order of each of the matric coefficients**A**is said to be a proper matric polynomial if_{0}, A_{1}, …. A_{m-1}, A_{m}G(x)**A**_{0}is non-singular. Also,**x**is called intermediate. We assume that it is commutative with every, matric coefficient.**The characteristic equation of a square matrix**Let

**A [a**be an_{ij}]**n × n**square matrix. Then**A – λ****I**_{n}, which is a matric polynomial of first degree in**λ**is called the characteristic matrix of**A**.The determinant

**| A – λ I**, which is an ordinary polynomial in_{n}|**λ**of nth degree is called the characteristic polynomial of**A**.The equation

**| A – λ I**,_{n}| = 0is called the characteristic equation of

**A**.**Characteristic roots or Latent roots or Eigen values**The roots of the characteristic equation

**| A – λ I**of_{n}| = 0**A**are known as the characteristic roots or latent roots or eigen values of**A**.**Services: -**Matric Polynomial Homework | Matric Polynomial Homework Help | Matric Polynomial Homework Help Services | Live Matric Polynomial Homework Help | Matric Polynomial Homework Tutors | Online Matric Polynomial Homework Help | Matric Polynomial Tutors | Online Matric Polynomial Tutors | Matric Polynomial Homework Services | Matric PolynomialSubmit Your Query ???

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