内积空间是数学中的线性代数里的基本概念，是增添了一个额外的结构的矢量空间。这个额外的结构叫做内积或标量积。内积将一对矢量与一个标量连接起来，允许我们严格地谈论矢量的“夹角”和“长度”，并进一步谈论矢量的正交性。内积空间由欧几里得空间抽象而来（内积是点积的抽象），这是泛函分析讨论的课题。

内积空间有时也叫做准希尔伯特空间（pre-Hilbert space），因为由内积定义的距离完备化之后就会得到一个希尔伯特空间。

在早期的著作中，内积空间被称作酉空间，但这个词现在已经被淘汰了。在将内积空间称为酉空间的著作中，“内积空间”常指任意维（可数或不可数）的欧几里德空间。

In linear algebra, an inner product space is a vector space with an additional structure called an inner product. This additional structure associates each pair of vectors in the space with a scalar quantity known as the inner product of the vectors. Inner products allow the rigorous introduction of intuitive geometrical notions such as the length of a vector or the angle between two vectors. They also provide the means of defining orthogonality between vectors (zero inner product). Inner product spaces generalize Euclidean spaces (in which the inner product is the dot product, also known as the scalar product) to vector spaces of any (possibly infinite) dimension, and are studied in functional analysis.