Mathematics · Linear Algebra
Rank-k Retained Spectral Energy Percentage Calculator
Calculate retained spectral energy percentage from sum of retained squared singular values and full squared frobenius norm.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=100a/b with sum of retained squared singular values=84 and full squared Frobenius norm=100.
- retained spectral energy percentage=84.
Understand Rank-k Retained Spectral Energy Percentage
One idea, three depths
Choose how deeply to explain Rank-k Retained Spectral Energy Percentage
Rank-k Retained Spectral Energy Percentage: Calculate retained spectral energy percentage from sum of retained squared singular values and full squared frobenius norm.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Rank-k Retained Spectral Energy Percentage to answer this question: calculate retained spectral energy percentage from sum of retained squared singular values and full squared frobenius norm? Enter sum of retained squared singular values and full squared Frobenius norm; the calculator shows retained spectral energy percentage. For example: sum of retained squared singular values=84 and full squared Frobenius norm=100 produce retained spectral energy percentage=84. The answer tells you retained spectral energy percentage.
Age 15Explain it to a 15-year-oldConnect it to the formula
Rank-k retained energy is the percentage of total squared singular-value energy kept by a truncated SVD. This page evaluates the relationship directly. The rule is c=100a/b. Its input values are sum of retained squared singular values, full squared Frobenius norm, and the main result is retained spectral energy percentage. For example: sum of retained squared singular values=84 and full squared Frobenius norm=100 produce retained spectral energy percentage=84.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated rank-k retained spectral energy percentage relation over the valid real-number domain stated below. The implemented relation is c=100a/b, evaluated from sum of retained squared singular values, full squared Frobenius norm to produce retained spectral energy percentage. Rank-k retained energy is the percentage of total squared singular-value energy kept by a truncated SVD. This page evaluates the relationship directly. Include exactly the selected leading singular values in the numerator.
Inputs and valid domain
- sum of retained squared singular values must be a finite real number.
- full squared Frobenius norm must be a finite real number.
Important boundary: Include exactly the selected leading singular values in the numerator.
The formula
c=100a/b
How the calculator works through it
It substitutes sum of retained squared singular values, full squared Frobenius norm into the formula and exposes every numerical step above. The main output is retained spectral energy percentage.
Read the result correctly
The retained spectral energy percentage is the direct answer to “calculate retained spectral energy percentage from sum of retained squared singular values and full squared frobenius norm.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
sum of retained squared singular values=84 and full squared Frobenius norm=100 produce retained spectral energy percentage=84.
Where this model stops being reliable
Include exactly the selected leading singular values in the numerator.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Rank-k Retained Spectral Energy Percentage works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Rank-k Retained Spectral Energy Percentage uses c=100a/b. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Vectors and components
Component notation helps you follow how Rank-k Retained Spectral Energy Percentage combines directional or indexed values.
Review this foundation about 6 min
Optional enrichment
- Matrices and linear transformations
Matrices place Rank-k Retained Spectral Energy Percentage inside the wider language of linear systems and transformations.
Review this foundation about 7 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read sum of retained squared singular values, full squared Frobenius norm.
- Evaluate the principal relationship: c=100a/b.
- Return retained spectral energy percentage and check the domain conditions described above.
Python
from math import *
def rank_k_spectral_energy_calculator(a, b) -> float:
return ((100.0 * a) / b)
assert abs(rank_k_spectral_energy_calculator(84, 100) - 84) < 1e-6 * max(1.0, abs(84))
C
#include <assert.h>
#include <math.h>
double rank_k_spectral_energy_calculator(double a, double b) {
return ((100.0 * a) / b);
}
int main(void) {
const double expected = 84;
const double actual = rank_k_spectral_energy_calculator(84, 100);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double rank_k_spectral_energy_calculator(double a, double b) {
return ((100.0 * a) / b);
}
int main() {
constexpr double expected = 84;
const double actual = rank_k_spectral_energy_calculator(84, 100);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double rank_k_spectral_energy_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global rank_k_spectral_energy_calculator
section .text
rank_k_spectral_energy_calculator:
push rbp
mov rbp, rsp
sub rsp, 48
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
mov rax, 0x4059000000000000
movq xmm0, rax
movsd [rbp-40], xmm0
movsd xmm0, [rbp-40]
mulsd xmm0, [rbp-8]
movsd [rbp-32], xmm0
movsd xmm0, [rbp-32]
divsd xmm0, [rbp-16]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = rank_k_spectral_energy_calculator(a, b)
result = ((100.0 * a) / b);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := ((100.0 * a) / b);
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations
Standards, reading and academic references
Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.
Algebra and Trigonometry 2e
Read the related free OpenStax mathematics chaptersCite this book
- APA 7
- Abramson, J. (2021). Algebra and trigonometry 2e. OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites
- MLA 9
- Abramson, Jay. Algebra and Trigonometry 2e. OpenStax, 2021, https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
- Chicago author-date
- Abramson, Jay. 2021. Algebra and Trigonometry 2e. Houston, TX: OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Rank-k Retained Spectral Energy Percentage Calculator. MW SysArc Tools. https://math.mwsysarc.com/linear-algebra/rank-k-spectral-energy-calculator
MLA 9
MW SysArc. “Rank-k Retained Spectral Energy Percentage Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/linear-algebra/rank-k-spectral-energy-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Rank-k Retained Spectral Energy Percentage Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/linear-algebra/rank-k-spectral-energy-calculator.
Harvard
MW SysArc (2026) ‘Rank-k Retained Spectral Energy Percentage Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/linear-algebra/rank-k-spectral-energy-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_rank_k_spectral_energy_calculator_2026,
author = {{MW SysArc}},
title = {Rank-k Retained Spectral Energy Percentage Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/linear-algebra/rank-k-spectral-energy-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Rank-k Retained Spectral Energy Percentage Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/linear-algebra/rank-k-spectral-energy-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Rank-k Retained Spectral Energy Percentage do?
Calculate retained spectral energy percentage from sum of retained squared singular values and full squared frobenius norm.
How does the Rank-k Retained Spectral Energy Percentage work?
The calculator applies c=100a/b. Rank-k retained energy is the percentage of total squared singular-value energy kept by a truncated SVD. This page evaluates the relationship directly.
What can I learn from the Rank-k Retained Spectral Energy Percentage?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .