Actually, I think it's very similar to Axler's in spirit. Not numerical at all (there is a description of the min squares problem, but that's it as far as I rem

Actually, I think it's very similar to Axler's in spirit. Not numerical at all (there is a description of the min squares problem, but that's it as far as I remember). Matrices are used more explicitely than in Axler, but only when necessary, because the author claims he's an operator theorist so the focus is on linear operators. Determinants are introduced as multi-linear functionals and are not avoided as in Axler. Supporting the fact that the book is quite theoretical, this is what you can find in the last chapters: Chapter 6. Structure of operators in inner product spaces. Chapter 7. Bilinear and quadratic forms Chapter 8. Dual spaces and tensors Chapter 9. Advanced spectral theory Unfortunately I'm not familiar with the Russian books.