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geometric object that has magnitude (or length) and direction. Euclidean vectors can be added and scaled to form a vector space. A vector quantity is a...

They have to be expressed by both magnitude and direction. Historically, vectors were introduced in geometry and physics (typically in mechanics) for quantities...

space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied ("scaled") by numbers called scalars...

a parasite or microbe, to another living organism. Agents regarded as vectors are mostly blood-sucking insects such as mosquitoes. The first major discovery...

vector spaces, a set of vectors is said to be linearly independent if there exists no nontrivial linear combination of the vectors that equals the zero vector...

space with an operation called an inner product. The inner product of two vectors in the space is a scalar, often denoted with angle brackets such as in...

the vector with respect to B. The elements of a basis are called basis vectors. Equivalently, a set B is a basis if its elements are linearly independent...

form of unit vectors. Unit vectors may be used to represent the axes of a Cartesian coordinate system. For instance, the standard unit vectors in the direction...

{\displaystyle \mathbb {C} ^{n}} , kets can be identified with column vectors, and bras with row vectors. Combinations of bras, kets, and linear operators are interpreted...

dimension of a vector space V is the cardinality (i.e., the number of vectors) of a basis of V over its base field. It is sometimes called Hamel dimension...

Vector may also refer to: Vector (mathematics and physics) Row and column vectors, single row or column matrices Vector quantity Vector space Vector field...

rotates, stretches, or shears the vectors upon which it acts. A linear transformation's eigenvectors are those vectors that are only stretched or shrunk...

In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant...

with vector fields or scalar functions: 0-vectors and 3-vectors with scalars, 1-vectors and 2-vectors with vectors. From the point of view of differential...

and integrative vectors like lentiviral vectors are commonly employed for gene therapy. Chimeric viral vectors—such as hybrid vectors with qualities of...

&a_{n}\end{bmatrix}}.} (Throughout this article, boldface is used for both row and column vectors.) The transpose (indicated by T) of any row vector is a column vector,...

four major types of vectors are plasmids, viral vectors, cosmids, and artificial chromosomes. Of these, the most commonly used vectors are plasmids. Common...

the same way. Contravariant vectors are often just called vectors and covariant vectors are called covectors or dual vectors. The terms covariant and contravariant...

by a constant velocity to another inertial reference frame).: ch1  Four-vectors describe, for instance, position xμ in spacetime modeled as Minkowski space...

angular velocity "vector" of the original object; for true vectors (also known as polar vectors), the reflection "vector" and the original "vector" must...