what are orthogonal vectors what are orthonormal vectors

what are orthogonal vectors

what are orthonormal vectors

what is rank of a matrix

what is nullity of a matrix

what is eigen vector

Expert Solution

1. Orthogonal vectors :

Two vectors are said to be orthogonal if they are perpendicular to each other. i.e. the dot product of the two vectors is zero.

2. Orthonormal vectors :

Two orthogonal vectors are said to be orthonormal if they are unit vectors.

3. Rank of a matrix :

A matrix of size m x n is said to be of rank r if the there exists at least one r th order minor which is non-zero and every (r+1) th order minor is zero.

4.Nullity of a matrix :

Let A be a matrix of size m x n then the dimension of the nullspace N(A) is called the nullity of the matrix A

5. Eigen vector :

A scalar λ is called an eigenvalue of the n × n matrix A is there is a nontrivial solution x of Ax = λx. Such an x is called an eigenvector corresponding to the eigenvalue λ.

milcah answered 2 years ago

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