How Do You Spell SUBSPACES?

Pronunciation: [sˈʌbspe͡ɪsɪz] (IPA)

The spelling of the word "subspaces" can be explained using IPA phonetic transcription. It is pronounced /ˈsʌbˌspeɪsɪz/, with stress on the first syllable. The "s" sound is followed by a short "u" sound, then a "b" sound. The second syllable is pronounced with a long "a" sound, followed by a soft "s" sound and an "i" sound. The final syllable is pronounced with a "z" sound. The word "subspaces" refers to a subset of a larger mathematical space.

SUBSPACES Meaning and Definition

1. Subspaces are a fundamental concept in linear algebra that pertains to vectors and vector spaces. A subspace is a subset of a vector space that retains certain properties of the vector space, allowing it to be considered a smaller vector space within the original space.

   To be considered a subspace, three conditions must be satisfied. Firstly, the subspace must contain the zero vector of the original space, as it is a necessary part of any vector space. Secondly, the subspace must be closed under addition, meaning that if two vectors are in the subspace, their sum must also be in the subspace. Lastly, the subspace must be closed under scalar multiplication, implying that if a vector is in the subspace, any multiple of that vector must also be in the subspace.

   These conditions ensure that the subspace preserves the vector space structure, enabling operations such as vector addition and scalar multiplication within the subspace. Furthermore, subspaces inherit some properties from the original space, such as linear independence and dimensionality. The dimension of a subspace is the maximum number of linearly independent vectors it contains.

   Subspaces provide a powerful tool for analyzing and solving problems related to vector spaces. They play a significant role in various fields, including quantum mechanics, computer science, and engineering, where vector spaces frequently arise.

Common Misspellings for SUBSPACES

• sunspacese
• sunspeces

Etymology of SUBSPACES

The word "subspace" is a compound word derived from the combination of the prefix "sub-" and the noun "space".

The prefix "sub-" comes from Latin, where it means "under" or "below". It is commonly used in English to indicate something that is of lesser degree, size, or importance than the main thing it is associated with.

The noun "space" comes from Old French "espace" and directly from Latin "spatium", meaning "distance", "expanse", or "room". In mathematics, "space" refers to a set of mathematical objects with certain properties.

So, when the prefix "sub-" is added to the noun "space", it forms the word "subspace", indicating a space that is smaller or contained within a larger space. In mathematics, subspaces often refer to subsets of vector spaces that retain certain properties of the larger space from which they are derived.