# Vector

Class

The `Vector` class represents a mathematical vector, which is useful in its own right, and also constitutes a row or column of a `Matrix`.

## `Method` Catalogue

To create a Vector:

To access elements:

To enumerate the elements:

Properties of vectors:

`Vector` arithmetic:

`Vector` functions:

Conversion to other data types:

String representations:

Attributes

#### elements

INSTANCE CREATION

Class Methods

Creates a `Vector` from a list of elements.

`Vector[7, 4, ...]`

Returns a standard basis `n`-vector, where k is the index.

```Vector.basis(size:, index:) # => Vector[0, 1, 0]
```

Creates a vector from an Array. The optional second argument specifies whether the array itself or a copy is used internally.

Returns `true` iff all of vectors are linearly independent.

```Vector.independent?(Vector[1,0], Vector[0,1])
=> true

Vector.independent?(Vector[1,2], Vector[2,4])
=> false```

`Vector.new` is private; use Vector[] or `Vector.elements` to create.

Return a zero vector.

```Vector.zero(3) => Vector[0, 0, 0]
```
Instance Methods

Multiplies the vector by `x`, where `x` is a number or a matrix.

No documentation available

`Vector` subtraction.

No documentation available

Returns `true` iff the two vectors have the same elements in the same order.

Returns element number `i` (starting at zero) of the vector.

No documentation available

Returns an angle with another vector. Result is within the [0…Math::PI].

```Vector[1,0].angle_with(Vector[0,1])
# => Math::PI / 2
```

Returns a copy of the vector.

The coerce method provides support for Ruby type coercion. This coercion mechanism is used by Ruby to handle mixed-type numeric operations: it is intended to find a compatible common type between the two operands of the operator. See also `Numeric#coerce`.

Collects (as in `Enumerable#collect`) over the elements of this vector and `v` in conjunction.

An alias for []

Creates a single-row matrix from this vector.

An alias for cross_product

Returns the cross product of this vector with the others.

```Vector[1, 0, 0].cross_product Vector[0, 1, 0]   => Vector[0, 0, 1]
```

It is generalized to other dimensions to return a vector perpendicular to the arguments.

```Vector[1, 2].cross_product # => Vector[-2, 1]
Vector[1, 0, 0, 0].cross_product(
Vector[0, 1, 0, 0],
Vector[0, 0, 1, 0]
)  #=> Vector[0, 0, 0, 1]
```
An alias for inner_product

Iterate over the elements of this vector

Iterate over the elements of this vector and `v` in conjunction.

An alias for []
No documentation available
No documentation available
No documentation available
No documentation available

Returns a hash-code for the vector.

Returns `true` iff all of vectors are linearly independent.

```Vector[1,0].independent?(Vector[0,1])
=> true

Vector[1,2].independent?(Vector[2,4])
=> false```

Returns the inner product of this vector with the other.

```Vector[4,7].inner_product Vector[10,1]  => 47
```

Returns the modulus (Pythagorean distance) of the vector.

```Vector[5,8,2].r => 9.643650761
```
An alias for collect

Like `Vector#collect2`, but returns a `Vector` instead of an Array.

An alias for magnitude

Returns a new vector with the same direction but with norm 1.

```v = Vector[5,8,2].normalize
# => Vector[0.5184758473652127, 0.8295613557843402, 0.20739033894608505]
v.norm => 1.0
```
An alias for magnitude

Returns a vector with entries rounded to the given precision (see `Float#round`)

An alias for []=
An alias for []=

Returns the number of elements in the vector.

Returns the elements of the vector in an array.

Return a single-column matrix from this vector

Returns `true` iff all elements are zero.