On the angle between two subspaces of an inner product space

Hendra Gunawan

doi:10.62918/hjma.v4i1.48

On the angle between two subspaces of an inner product space

Authors

Hendra Gunawan Institut Teknologi Bandung

DOI:

https://doi.org/10.62918/hjma.v4i1.48

Keywords:

Angle between two subspaces, inner product spaces

Abstract

In this paper, we shall discuss two formulae for the angle between two subspaces, or more generally the angle from a subspace of dimension $p$ to another subspace of dimension $q$ with $1\le p\le q\le \dim(X)$, in an inner product space $X$. In particular, we shall see that the two seemingly different formulae, one is obtained by H. Gunawan, O. Neswan, and W. Setya-Budhi in 2005 and the other by N. Wildberger in 2017, are actually identical.

References

H. Gunawan, On $n$-inner products, $n$-norms, and the Cauchy-Schwarz inequality, Sci. Math. Japon. 5 (2001), 47--54.

H. Gunawan, Mashadi, On $n$-normed spaces, Int. J. Math. Math. Sci. 27 (2001), 631--639.

H. Gunawan, O. Neswan, W. Setya-Budhi, A formula for angles between subspaces of inner product spaces, Beitrage Alg. Geom. 46 (2005), 311--320.

I. B. Risteski, K. G. Trencevski, Principal values and principal subspaces of vector spaces with inner products, Beitrage Alg. Geom. 42 (2001), 289--300.

N. J. Wildberger, Rational trigonometry in higher dimensions and a diagonal rule for 2-planes in four-dimensional space, KoG 21 (2017), 47--54.

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Published

22-05-2025

How to Cite

Gunawan, H. (2025). On the angle between two subspaces of an inner product space. Hilbert Journal of Mathematical Analysis, 4(1), 001–005. https://doi.org/10.62918/hjma.v4i1.48