# Are all eigenvectors linearly independent?

Any two

**eigenvectors**are**linearly independent**. FALSE. Any nonzero scalar multiple of an**eigenvector**is also an**eigenvector**. However, two**eigenvectors**corresponding to different eigenvalues must be**linearly independent**.A.

### What is a normalized vector?

The

**normalized vector**of is a**vector**in the same direction but with norm (length) 1. It is denoted and given by. where is the norm of . It is also called a unit**vector**.#### What does it mean to normalize data?

In the simplest cases,**normalization**of ratings**means**adjusting values measured on different scales to a notionally common scale, often prior to averaging. Some types of**normalization**involve only a rescaling, to arrive at values relative to some size variable.#### What is the norm of a vector?

In linear algebra, functional analysis, and related areas of mathematics, a**norm**is a function that assigns a strictly positive length or size to each**vector**in a**vector**space—save for the zero**vector**, which is assigned a length of zero. A**vector**space on which a**norm**is defined is called a normed**vector**space.#### What is the cultural norm?

The difference has to do with**cultural norms**. The term '**culture**' refers to attitudes and patterns of behavior in a given group. '**Norm**' refers to attitudes and behaviors that are considered normal, typical or average within that group.

B.

### What are the eigenvectors?

**Eigenvalues**and

**eigenvectors**. Geometrically an

**eigenvector**, corresponding to a real nonzero

**eigenvalue**, points in a direction that is stretched by the transformation and the

**eigenvalue**is the factor by which it is stretched. If the

**eigenvalue**is negative, the direction is reversed.

#### What are eigenvalues in quantum mechanics?

The function is called an eigenfunction, and the resulting numerical value is called the**eigenvalue**. Eigen here is the German word meaning self or own. It is a general principle of**Quantum Mechanics**that there is an operator for every physical observable. A physical observable is anything that can be measured.#### What are the eigenvalues of a matrix?

A·v=λ·v. In this equation A is an n-by-n**matrix**, v is a non-zero n-by-1 vector and λ is a scalar (which may be either real or complex). Any value of λ for which this equation has a solution is known as an**eigenvalue**of the**matrix**A. It is sometimes also called the characteristic value.#### What are the characteristics of polynomials?

**Characteristic polynomial**. In linear algebra, the**characteristic polynomial**of a square matrix is a**polynomial**which is invariant under matrix similarity and has the eigenvalues as roots. It has the determinant and the trace of the matrix as coefficients.

Updated: 17th October 2019