Baswanth Oruganti

Can you suggest a geometric way of looking at the Transpose or Conjugate Transpose of a Matrix? Below, I am putting together a thread with responses of @3blue1brown to my question.

The quadratic formula is much more than a math class rite of passage. It’s a mathematical triumph that spans across millennia, evolving from ancient Babylonian clay tablets to the brilliant, formalized methods of the 7th-century mathematician Brahmagupta.

33% of 850 is 280, a hundred more than 33% of 543, which is 180. By opposing the Constitutional Amendment Bill, the Opposition has not only delayed women’s reservation till 2034, but also reduced the number of seats women could have got in the LS. What a blunder. Someone seriously needs to enlighten the Congress led Opposition otherwise people will fix them in the same place for the next 50 years. #Parliament #LokSabha #WomenReservation

Show an equation that looks crazy

By blocking the Women’s Reservation Bill, the Congress-led opposition has denied India a historic step toward women’s empowerment. This is not just political obstruction, it is a betrayal of millions of women who deserve equal voice and rightful representation in Parliament. The nation will remember.

Opposing parties should seriously question themselves; what have they achieved ? While the reality is that the numbers would come down for the south and women reservation bill has been postponed ! Justice is rendered neither to the south nor the women! If 2026 census were to come the situation would be worse off for the south, further penalised for being disciplined in the matters of family planning.

Pauli Matrices: They explain how quantum particles like electrons carry an invisible “arrow” called spin, and how this spin behaves when measured or rotated. Imagine spin as a tiny compass needle—but instead of pointing just north or south, it can exist in a blend of directions

Now that the 131st Amendment Bill failed, allocation of Lok Sabha seats will be based on 2026 census data. As per current estimates, seven States will likely lose 35 seats: AP (-5), Telangana (-3), TN (-10), Karnataka (-2), Kerala (-7), Odisha (-4), and WB (-4). Four States will likely gain 34 seats: UP (+12), Bihar (+10), MP (+5), and Rajasthan (+7). BJP is widely believed to be the potential beneficiary of redistribution of seats to States based on 2026 population. In a stunning act of self-denial, the NDA government came forward to freeze the current share of States based on the 1971 census data. There could be many reasons for BJP committing to such a freeze - putting the nation above the party, paving the way for expanding their footprint in the South, or avoiding a divisive issue when the nation has to focus on growth and prosperity in the face of global challenges. Whatever be the motivation of BJP, the seven States that lost share of population are offered an unexpected gift. You don't look a gift horse in the mouth! Surprisingly, the parties which have great stakes in the South and East have scored a spectacular self goal. This is a classic case of cutting the nose to spite the face. In 2001, as the freeze in seats was expiring, I was deeply involved in persuading the then Vajpayee government to continue the freeze in the number of seats allocated to States for another 25 years. An unwieldy coalition and the economic challenge posed by external sanctions after the Pokharan explosion demanded national unity, and the parties responded with the 84th Amendment. Now again a priceless opportunity arose, and the Opposition squandered it without any strategic thinking. If political animosity makes you oblivious of your own interest, or larger interests of fostering unity and focusing on growth and harmony, it is a sign of dysfunctional politics. I appeal to all parties to come together and find a harmonious solution to the thorny problem of seats allocation in the face of demographic imbalances. National unity and our quest for opportunity and prosperity for all demand a fair and swift resolution. In the long run migration will resolve the imbalances. Already millions of migrant workers are building and sustaining the economies of several States in the South, West and North. That is why, despite low fertility rate, Maharashtra's share of the population is increasing. In the US, dramatic internal migration changed the demography and representation over the years. People move freely to States where there is growth and jobs are created. In a century, Florida increased its representation in the US Congress from 4 to 28, California from 11 to 52, Texas from 18 to 38, and Washington from 5 to 10. Owing to outward migration, New York lost seats, from 43 to 26, Pennsylvania from 36 to 17, Illinois from 27 to 17, Ohio from 22 to 15, and Missouri from 16 to 8. We should make it easy for people to migrate to other States and recognize and respect their constitutional rights everywhere and make their life easier and safe. That will resolve our demographic challenges. Most states reached low fertility levels, and Bihar, UP, MP, Rajasthan and Jharkhand too are going to reach there in a few years. We need a reasoned and pragmatic approach to grow together and become strong. Let us persuade parties to shed inflammatory and divisive rhetoric and focus on quality education and skills and opportunities for all.

3D visualization of Euler’s formula.

Sink (left, div < 0; everything collapses inward), Source (middle, div > 0; pure explosion outward), Incompressible (right, div = 0; swirls forever with zero net loss). Textbooks never made the flow rates feel this alive.

In this mesmerizing y=Ax video, eigenvectors glow with brilliance! As you rotate the vector x, Ax traces the ellipse perfectly. But the eigenvector lights up—no rotation at all, just pure scaling by its eigenvalue!

A Visualization ò Stokes’ Theorem

Volume of a Sphere: Spherical Coordination.

Elementary Rotation Matrices.

The angle between two planes is the angle between their normal vectors.

Gradient descent is a method used to find the best or minimum value of a function. Imagine standing on a hill and trying to reach the lowest point in the valley. The simplest way is to take small steps downhill in the steepest direction. Gradient descent works in a similar way. Starting from an initial guess, it repeatedly moves in the direction that decreases the value of the function the fastest. This idea is widely used in machine learning and data science to train models and improve predictions.

Mathematics may appear harsh in the beginning, but as you discover its inner beauty, it becomes a source of endless joy.

Reminder: - MSE you use when you don’t have outliers - RMSE you use when you want to interpret the above better - MAE you use when you have positive/zero/negative values and outliers - MAPE you use when you only have positive values and emphasize interpretability - RMSLE you use for positive values with nonnormal distribution - wMAPE you use when you want MAPE but have large vs small values - sMAPE you use when you want MAPE but have zero/negative values - R2 you use because your boss only knows this one

Prof. Donald Knuth opened his new paper with "Shock! Shock!" Claude Opus 4.6 had just solved an open problem he'd been working on for weeks — a graph decomposition conjecture from The Art of Computer Programming. He named the paper "Claude's Cycles." 31 explorations. ~1 hour. Knuth read the output, wrote the formal proof, and closed with: "It seems I'll have to revise my opinions about generative AI one of these days." The man who wrote the bible of computer science just said that. In a paper named after an AI. Paper: cs.stanford.edu/~knuth/papers/…

Jacobian is the matrix of partial derivatives for a multivariable mapping. It is the best linear approximation. It tells how small input changes create output changes. Its determinant tells local area or volume scaling.

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