This definition of expectation as inner product can be extended to random vectors as well.

The wedge product and dot product can be combined (through summation) to form the geometric product.

For real random variables and , the expected value of their product formula_35 is an inner product.

In linear algebra, an inner product space is a vector space with an additional structure called an inner product.

Scalar triple product The scalar triple product (also called the mixed or box product) is defined as the dot product of one of the vectors with the cross product of the other two.

In mathematics, the dot product, or scalar product (or sometimes inner product in the context of Euclidean space), is an algebraic operation that takes two equal length sequences of numbers (usually coordinate vectors) and returns a single number.

Recalling that two vectors are perpendicular if and only if their dot product is zero, it follows that the desired plane can be described as the set of all points formula_6 such that formula_11(The dot here means a dot product, not scalar multiplication.

In mathematical analysis, an isomorphism between two Hilbert spaces is a bijection preserving addition, scalar multiplication, and inner product.

In particular, if A and B are orthogonal, then the angle between them is 90 and formula_5At the other extreme, if they are codirectional, then the angle between them is 0 and formula_6This implies that the dot product of a vector A by itself is formula_7which gives formula_8the formula for the Euclidean length of the vector.

I went climbing in the Alps.

I tried climbing the mountain.

Tom loves to climb mountains.

I want to hike up this mountain.

I need to climb the tree.

Squirrels love climbing trees.

It's dangerous to climb this mountain.

It's dangerous to climb this mountain.

I want to climb Mt. Fuji.

I cannot climb this mountain.

This mountain is difficult to climb.

Climbing this mountain is very difficult.

I want to climb Mt. Fuji.

They began to climb the hill.

Pressure is a scalar quantity.

It was a bit like climbing a mountain.

I've always wanted to climb Mt. Fuji.

Climbing that mountain was a piece of cake.

He has no trouble climbing trees.

Despite our difficulties, we managed to climb the mountain.

It is the ratio of the mapped point's scale to the nominal scale.

Average speed does not describe the speed variations that may have taken place during shorter time intervals (as it is the entire distance covered divided by the total time of travel), and so average speed is often quite different from a value of instantaneous speed.

For centered data (i.e., data which have been shifted by the sample mean so as to have an average of zero), the correlation coefficient can also be viewed as the cosine of the angle formula_34 between the two vectors of samples drawn from the two random variables (see below).

You can hike for days and not encounter anybody.

I think it's dangerous to climb that mountain alone.

Whether this tag affects font scaling

You need good equipment to climb that mountain.

For instance the dot product of a vector with itself would be an arbitrary complex number, and could be zero without the vector being the zero vector (such vectors are called isotropic) this in turn would have consequences for notions like length and angle.

You want to climb through at night when the ice is frozen.

As we passed, two boys were climbing the mount Kenya of trash.

For a person who is in good physical condition, climbing mountains is a cinch.

Prey is obtained by hunting either on the ground or in the trees.

And that way you can scale things much smaller than microchips.

What goals is this ant trying to achieve by climbing this blade of grass?

In the product topology, the closure of a product of subsets is equal to the product of the closures.

What product is that?